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Photon small-field measurements with a CMOS active pixel sensor
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Phys. Med. Biol. 60 4383 (http://iopscience.iop.org/0031-9155/60/11/4383) View the table of contents for this issue, or go to the journal homepage for more
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Institute of Physics and Engineering in Medicine Phys. Med. Biol. 60 (2015) 4383–4398
Physics in Medicine & Biology doi:10.1088/0031-9155/60/11/4383
Photon small-field measurements with a CMOS active pixel sensor F Jiménez Spang1, I Rosenberg2, E Hedin3 and G Royle1 1
Department of Medical Physics and Bioengineering, University College London, Gower Street, London WC1E 6BT, UK 2 UCLH NHS Foundation Trust, 250 Euston Road, London NW1 2PQ, UK 3 Department of Radiation Physics, Sahlgrenska Universitetssjukhuset, 41345 Göteborg, Sweden E-mail: [email protected] Received 3 February 2015, revised 27 March 2015 Accepted for publication 14 April 2015 Published 18 May 2015 Abstract
In this work the dosimetric performance of CMOS active pixel sensors for the measurement of small photon beams is presented. The detector used consisted of an array of 520 × 520 pixels on a 25 µm pitch. Dosimetric parameters measured with this sensor were compared with data collected with an ionization chamber, a film detector and GEANT4 Monte Carlo simulations. The sensor performance for beam profiles measurements was evaluated for field sizes of 0.5 × 0.5 cm2. The high spatial resolution achieved with this sensor allowed the accurate measurement of profiles, beam penumbrae and field size under lateral electronic disequilibrium. Field size and penumbrae agreed within 5.4% and 2.2% respectively with film measurements. Agreements with ionization chambers better than 1.0% were obtained when measuring tissue-phantom ratios. Output factor measurements were in good agreement with ionization chamber and Monte Carlo simulation. The data obtained from this imaging sensor can be easily analyzed to extract dosimetric information. The results presented in this work are promising for the development and implementation of CMOS active pixel sensors for dosimetry applications. Keywords: CMOS active pixel sensors, small-field dosimetry, Monte Carlo simulation, photon transfer curves, geant4 (Some figures may appear in colour only in the online journal) 1. Introduction As the radiation field becomes smaller techniques used for dosimetry of standard-size radiation fields are no longer valid (Das et al 2008). Loss of charged particle equilibrium and 0031-9155/15/114383+16$33.00 © 2015 Institute of Physics and Engineering in Medicine Printed in the UK
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volume averaging cause beam calibration to become inaccurate when the detector size is comparable to the radiation field, making the determination of dose questionable at best (Sibata et al 1991, Duggan and Coffey 1998). Miscalculation of dose due to inappropriate detector size can have clinical consequences for the outcome of treatments (Laub and Wong 2003). The use of dosimeters with high spatial resolution is therefore required (Das et al 2000, Jang et al 2011). Even though ionization chambers are the gold standard for radiation dosimetry, they present limitations to accurately measure small-field dosimetric parameters (McKerracher and Thwaites 1999, Martens et al 2000, Laub and Wong 2003). Several detectors have been proposed for small-field measurements. McKerracher and Thwaites (1999) found that no single detector was ideal for measurements of the small fields investigated in their study. Laub and Wong (2003) studied the effect of detector size for small fields using a p-type silicon diode, a 3 mm3 diamond detector and a set of ionization chambers and film. They found significant discrepancies for profile and output factor measurements of small fields and concluded that the limited spatial resolution of the detectors leads to inaccuracies in the commissioning of IMRT. Sauer and Wilbert (2007) investigated several detectors for small-field output factor measurements and calculated corrections for solid state detectors. Pappas et al (2008) compared several detectors with a silicon-diode array and found that detector size and detector composition, as well as positioning difficulties are the main problems related to small field profile measurements. More recently, Monte Carlo techniques have been used to calculate correction factors in small fields. Scott et al (2012) calculated density-correction factors for ion chambers and solid-state detectors. They found that changes in those factors with field size were due to differences between detector materials and water. Benmakhlouf et al (2014) use Monte Carlo simulations to calculate output correction factors of several detectors on a 6 MV beam. In this paper the application of CMOS active pixel sensors (CMOS APS) (Fossum 1997, Bigas et al 2006) for the dosimetry of small photon fields is presented. CMOS sensors have the advantage of very small pixel size and the capability to provide two-dimensional information and fast readout. CMOS APS are formed from an array of pixels. Each pixel is a radiation sensitive element with a photodiode, a capacitor and three transistors. CMOS sensors are described as active because they contain at least one active device per pixel, allowing the charge to be directly transferred from the pixel to the output by randomly addressing each pixel. A row-based readout architecture provides random access to pixels avoiding charge transfer over long distances as occurred in CCD readout technology. This makes CMOS sensors more suitable for dosimetry applications. The device used in this work, Vanilla (Blue et al 2007), is a 25 µm pixel pitch sensor which provides sufficient spatial resolution for small field measurements. Beam profiles and tissue phantom ratios were measured and compared with ionization chamber measurements and Monte Carlo simulations. It is demonstrated that CMOS APS have the potential to measure dosimetric parameters of small-photon beams accurately and overcome the main problems related to small field measurements, in particular positioning difficulties and limited high spatial resolution. 2. Materials and methods 2.1. Linear accelerator
A clinical linear accelerator model Varian 2100CD (Varian, Palo Alto, CA) was used for all measurements. The Varian 2100CD produces x-ray beams with photon energies of 6 and 10 MV. Square fields from 0.5 × 0.5 cm2 to 25 × 25 cm2 at a source-to-axis distance (SAD) of 4384
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Figure 1. Architecture of the Vanilla sensor (left) and pixel (right).
100 cm were produced using the collimator jaws. The Monitor Units (MU) were calibrated to deliver 1 cGy MU−1 at 95 cm source-to-surface distance (SSD) and a depth of 5 cm in water for a 10 × 10 cm2 field. 2.2. Detector system
The sensor and the pixel architectures are shown in figure 1. The sensor has two operation modes. In the digital mode, the analog to digital conversion of the voltage inside the pixel is performed by the on-chip ADCs. There are 130 ADCs on-chip to perform a 12-bit successive approximation conversion. In the analog mode the voltage signal in the pixel is converted using a 12-bit ADC on an expansion board. Image acquisition and control of the sensor were performed through the MI-3 OptoDAq system. This system was based on a Memec Virtex-II Pro™ 20FF1152 FPGA development board which generated the required control signal for the sensor. Further details can be found in Blue et al (2007). Three transistors and a photodiode (PD) are present inside the pixel. The transistor MRST is used to reset the pixel, MIN is the buffer and MSEL is used to select the readout of the pixel. After ionizing radiation interacts in the pixel sensitive volume, the generated electrons are collected by the diodes implanted into the pixel volume due to charge diffusion (Turchetta et al 2001, Kleinfelder et al 2002). The collected charge is integrated by the action of a capacitor in each pixel. This charge is then transferred to the column output through the charge amplifier by clocking the row selectors sequentially allowing the full image to be progressively read out from the pixels. The column output is then serially transferred by a readout register to an analog-to-digital converter to finally form the image which is analyzed to extract dosimetric information. 2.3. Sensor calibration
The sensor was optically calibrated through photon transfer (PT) curves (Bohndiek et al 2008) to convert ADC outputs to absolute units (e−) through the ADC sensor conversion gain 4385
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Figure 2. Schematic of the experimental setup used for the sensor characterization.
KADC(e−/DN), where DN represents computer digital number units. This calibration also helped us correct the intrinsic nonlinearities present in CMOS imagers (Janesick 2007). By characterizing the sensor signal in terms of electron units a direct connection with dosimetry can be achieved. In addition, a full determination and quantification of sources of noise can be obtained from the same analysis. The sensor was placed inside a metallic black box (figure 2) and stimulated by a 520 nm narrow-band light emitter diode (LumiLED) coupled with two white diffusion sheets (Lee Filters, white 129) with 87% attenuation. A lens was placed in front of the LED to focus light intensity across the sensor surface. Light intensity was varied by changing the voltage across the LED to cover the dynamic range of the sensor. The voltage was uniformly varied from 2.16 V up to 19.68 V to achieve sensor saturation using steps of 0.08 V. From the collected data the sensitivity K(e−/DN) was calculated as S (DN) K (e− /DN) = (1) σS (DN)2 − σR(DN)2
where S (DN) is the signal in digital numbers (DN), σR(DN) is the read noise, and σS(DN) is the total noise. The difference σS(DN)2 − σR(DN)2 is the shot noise. The total noise is found from ⎧ ⎫1/2 S (DN) 2 ⎬ [ (DN) ] P S σS (DN) = ⎨σR(DN)2 + + (2) N ⎩ ⎭ K (e− /DN)
where the last term is the fixed pattern noise (FPN) and PN is called the quality factor, which is approximately 0.02 for CMOS and CCD sensors (Janesick 2007). For equation (2) to be useful, shot noise must be isolated. By subtracting two consecutive frames at the same illumination level the FPN is removed. Read noise is found from the intercept in the PT curve and subtracted from the remaining term in equation (2). Once shot noise is isolated, the sensor parameters can be determined. The set of equations used to generate PT data are given below: 1 S¯k = ∑ Sik, j. (3) LM i, j 1 S¯ = (S¯A + S¯B ) − S¯D. (4) 2 4386
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1 σS2 = ∑ [(SiA, j − S¯A) − (SiB, j − S¯B )]2 . (5) 2(N − 1) i, j
where S¯k is the mean frame, L and M are the number of rows and columns in the frame, respectively, S¯A and S¯B are two consecutive frames that must be subtracted to remove fixed pattern noise, and σS2 is the signal variance. The indexes of summation i and j go from 0 to L − 1 and 0 to M − 1, respectively. For the correction of the sensor nonlinearities photon flux measurements had to be accurately determined. A calibrated photodiode (Hamamatsu S1336-5BQ) was placed at the same position of the sensor after image acquisition. The output current, which is proportional to the photon flux input signal, was measured using a Keithley 237 High Voltage Source-Measure Unit. Over a hundred measures were averaged to obtain the output current that corresponded to each illumination level to calculate the total number of incident photons per pixel during the sensor integration time. This data was then applied to the data collected from equations (3) to (5) and a corrected conversion gain (SADC(e−/DN)) was calculated from KADC(e−/DN), the signal and the incident photons per pixel. To quantify how much x-ray shot noise limits sensor performance, signal-to-noise ratio (SNR) was calculated from SNR =
S
σTOTAL (6) S = 2 + ηiS + (PN S )2]1/2 [σREAD
where ηi is the quantum yield and S the signal. From equation (6) it can be seen that SNR within the shot noise regime is proportional to the square root of signal. Shot noise limits the signal-to-noise performance when detected signals are large, which represents a fundamental limit for imaging sensors. 2.4. Measurements
Dosimetric parameters such as beam profiles, tissue-phantom ratios (TPRs) and output factors were measured with the Vanilla sensor at 6 and 10 MV photon energies and compared with ionization chamber, film measurements and Monte Carlo (MC) simulations. To prevent sensor saturation, the dose rate of the linear accelerator was restricted throughout to 100 MU min−1 and the sensor was run at 55 frames per second with an integration time of 18 ms. Before measurements a dark image was averaged over 100 frames to correct for the offset signal. The offset signal comprised mainly read noise, but also any stimulus input signal present during measurements. This dark image was then subtracted from all measurements. For all measurements the sensor was embedded in a slab of Perspex of size 30 × 30 × 1 cm3 as shown in figure 3. Slabs of Solid Water (SW) totalling 4 cm thick were placed on top to obtain a total build-up of 5 cm, to eliminate electron contamination. A SW slab of 10 cm was used for backscatter. 2.4.1. Beam profiles. Beam profiles for 6 and 10 MV photon beams with 0.5 × 0.5 cm2 fields
were imaged with the Vanilla sensor in SW. Profiles were also measured with radiographic X-OMAT V film and MC simulations for comparison. A Vidar film digitizer (VXR-16, Vidar Systems Corp., Herndon, VA) was used to scan the film. The film scanner was operated with a resolution of 300 dpi and a depth of 12 bits. 4387
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Figure 3. Experimental setup for dosimetric parameter measurements.
The sensor was placed in SW slabs at depths from 5 to 25 cm, but at a constant source to detector distance of 100 cm. A set of 100 frames were averaged to get a final image which was then analyzed using Matlab and ImageJ to generate the beam profiles. The small 0.5 × 0.5 cm2 beam profile was measured with film and the CMOS sensor after measuring the output factor for the same field, without moving the collimators to avoid collimator positional erros. 2.4.2. Tissue-phantom ratios (TPRs). TPRs are defined as the ratio of the signal at a given depth to a reference depth of 10 cm, with a field size of 10 × 10 cm2 at a constant SAD. The signal was integrated in a region of interest (ROI) of 1 mm2 at the centre of the sensor array. The mean number of electrons was calculated by converting the average signal in the ROI to electrons through the ADC signal sensitivity. TPRs were also measured using a Farmer ionization chamber for comparison with the CMOS sensor results. 2.4.3. Output factors. Output factors measured with the sensor were calculated as the ratio of the average pixel signal over a ROI of 40 × 40 pixels to a reference field of 10 × 10 cm2, at 10 cm deep at the isocentre in the phantom. The linear accelerator was operated at 100 MU min−1 for sensor measurements to prevent sensor saturation and at 600 MU min−1 when measuring with the Farmer ionization chamber. Ionization chamber measurements were done for fields between 4 × 4 cm2 and 25 × 25 cm2. Comparisons were done with simulated OFs obtained from the work by Hedin et al (2010) at SSD 90 cm and SAD 100 cm. Dose values for OF were calculated in two different ways; directly from the energy deposited in a voxel and from dose values obtained from a fifth order polynomial fitted to the depth dose curves for depths between 5 cm and 20 cm. 2.4.4. Monte Carlo simulations Phase-space files. As no appropriate detectors for small field dosimetry was in use at the
Radiotherapy Department at UCLH at the moment of this work, Monte Carlo simulations were performed to compare a set of TPRs measured with the sensor to MC-simulated TPRs for a small 6 MV 0.5 × 0.5 cm2 beam. The simulations were performed using the GEANT4 9.2 4388
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Table 1. Composition and thickness of the layers simulated in the model of the sensor.
Layer
Composition
Thickness (μm)
Pasivation Silicon dioxide Aluminum Epitaxiala Substrate PCBb
SiNO3 SiO2 Al Si Si SiO2 (70%) C15O2H16 (23%) C3H6O (7%) Cu
1 4 1 14 500 1664
Copper in PCB
35
Note:a Sensitive volume. b Printed Circuit Board.
implementation of PENELOPE, with all electron transport parameters optimized as described in Elles et al (2008). The dose values were scored in cylinders of radius 0.05 cm and height 0.3 cm at the central axis of a water phantom of dimensions 30 × 30 × 20 cm3. Simulations were repeated three times to estimate uncertainties. The incident spectrum was obtained from a collection of 6 MV phasespace files of a Varian linear accelerator Clinac iX published on the IAEA NAPC Nuclear Data Section web site (Hedin et al 2010), and selected as representative of our Varian 2100CD. The linac MC modelling was based on 5.7 MeV monoenergetic electrons impinging on the target normally with a Gaussian spatial distribution of 0.1 cm. To determine the validity of this comparison, quality indexes (TPR10 20) of both the Varian 2100CD and the phase-space file were compared. Additionally, a 0.5 × 0.5 cm2 field was simulated in water and compared with a filmmeasured profile at similar conditions. This simulation setup consisted of an array of 52 × 52 voxels of area 0.025 × 0.025 cm2 and 0.1 cm thick at 10 cm deep at the origin of the water phantom. The uncertainty in the field size was estimated as half of the off-axis distance from the origin to the voxel centre. Sensor simulation. The sensor was precisely modelled using GEANT4 to score a dose beam profile of the small 6 MV 0.5 × 0.5 cm2 field in the sensor sensitive layer. This profile field size was then compared with actual measurements. The sensor was modelled as a layered detector consisting of six different layers. Table 1 shows the composition and thickness of the layers used in the Monte Carlo model according to information provided by the designers of the detector. The sensitive layer of the detector was divided in voxels of area 25 × 25 µm2 and height 14 µm to mimic the pixel pitch of the actual sensor. Energy deposited was scored in 520 × 520 voxels in the sensitive layer. As the sensitive volume of the detector was very thin (14 µm), we set the electron cut-off in this layer to 100 eV. In the Solid Water phantom the electron cut-off was set to a large value to stop the production of secondary electrons and allow a continuous-slowing-down energy deposition. This also reduced the simulation time.
3. Results 3.1. Sensor calibration
Figure 4(a) shows the PT curves with all sources of noise shown independently. The read noise, which is a signal-independet noise, was calculated from an analysis performed on 4389
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(a)
(b)
Figure 4. Photon transfer results: (a) photon transfer curve derived from measurements with the Vanilla sensor, (b) false signal versus the true signal based on SADC(e−/DN).
different regions of interest (ROIs) over the dark frames. A value σREAD = 2.63 ± 0.02 DN was estimated. From the raw data plotted in figure 4(a) it was noted that the shot noise curve deviates from the typical 0.5 slope on a Log–Log graph, indicating that the ADC sensitivity KADC(e−/DN) is dependent on signal level and therefore nonlinear. This sensitivity varies from 17.83 e−/DN to 23.04 e−/DN showing a maximum nonlinearity of 29%. The effect of this nonlinearity on the signal is shown in figure 4(b) where the false signal (calculated from KADC(e−/DN)) is compared with the true signal (corrected from SADC(e−/DN)). The new ADC signal sensitivity SADC(e−/DN) was found through a nonlinear compensation by using the incident photon flux on the pixel array to progressively correct the nonlinearity of the signals at higher levels, from the very first signal (Bohndiek et al 2008). From this procedure corrected PTC curves were generated, and additionally, all pixel values from all images were also corrected. For estimating read noise, KADC(e−/DN) at the very first signal level was used, resulting in σREAD = 47 ± 1e−. Figure 5 compares all sources of noise as a function of signal. For most of the dynamic range of the sensor the total noise represents about 2.2% of the signal. Note that FPN dominates at higher signal levels accounting for 2.0% of the signal. From the FPN curve the quality factor resulted in PN = 0.020 (2.0%), which allows us to express the FPN as FPN = 0.020 × S, where S is the signal. 3.2. Monte Carlo simulations Phase-space files. The first comparison made for the phase-space file validation was the
quality index of the machines (QI) or TPR20/10 measured for a 10 × 10 cm2 field. This comparison was made between the quality control data of four linear accelerators available at UCLH and MC simulations with the phase-space files. The average QI calculated with data from our four linear accelerators was 0.6644 ± 0.0015, which is in good agreement, within the statistical uncertainties, with the result obtained from the 6 MV phase-space file simulation, 0.6636 ± 0.0062. This is a good indication that the phase-space file produced a similar beam quality as the beams used in the measurements. Figure 6(a) compares the simulated beam profile in water and that measured with film for the 0.5 × 0.5 cm2 field at 10 cm deep. Field sizes calculated from the Monte Carlo-simulated small field and from the measured profile were in excellent agreement. From the Monte Carlo 4390
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Figure 5. Comparison of sources of noise plotted independently as function of signal.
Figure 6. Profiles for a 6 MV 0.5 × 0.5 cm2 field at 10 cm deep in phantom. (a)
Comparison of MC-simulated profile in water and film-measured profile in Solid Water, (b) comparison of MC-simulated profile in the sensitive layer of the sensor and measured with film in Solid Water.
simulation a value 5.1 ± 0.2 mm was obtained for field size. The corresponding field size measured with film was 5.10 ± 0.04 cm. This comparison shows an excellent match between the Monte Carlo beam model for the smallest field and the experimental beam of the Varian 2100CD. Sensor simulation. Figure 6(b) shows the simulated profile in silicon compared to the corresponding film-measured profile. Because of the low efficiency obtained during the simulation of this thin detector, the particles of the phase-space file were recycled 300 times. To reduce the statistical fluctuations, the beam profile was plotted by averaging (vertically) the dose deposited in 21 rows of pixels, from which 10 were above and below the central row of the detector array. The resulting profile was taken as representative of the dose profile in the central row. The profile was then smoothed using a Savitzky–Golay filter available in Matlab. 4391
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(a)
(b)
Figure 7. Beam profiles mesured in Solid Water with the CMOS sensor for a field size
0.5 × 0.5 cm2. The profiles were plotted from a single row of pixels across the sensor array, (a) 6 MV beam, (b) 10 MV beam.
A field size 5.12 ± 0.01 mm was obtained from the MC-simulated sensor, which agreed well with film (0.8%). Similarly, penumbra widths were in good agreement. The MC-simulated penumbra resulted in 1.92 ± 0.01 mm, compared with a film-measured penumbra of 1.86 ± 0.04 mm, which differed by 3.2%. From these results, it was determined that the phase-space file of the 0.5 × 0.5 cm2 field as well as the Monte Carlo modelling of the sensor were accurate for the comparisons presented in the following sections. 3.3. Beam profiles
Figure 7 shows the beam profiles measured with the CMOS sensor at different depths in SW. The ADC signal was converted to e− to correct for sensor nonlinearities. Profiles variations with depth and beam energy can be noted by comparing the graphs. Pixel response non-uniformity and fixed pattern noise effect can be observed more clearly from the 10 MV profiles, where the same fixed pattern on the profiles were reproduced at all depths. This can, however, be corrected by applying a smoothing filter on the data. Figure 8 comparesthe beam profiles for a 0.5 × 0.5 cm2 field measured with the CMOS sensor and film at 10 cm deep. Their agreement was evaluated by comparing the 20%–80% penumbra width and field size (full width at half maximum, FWHM). As shown in table 2, the field size of the small 6 MV beam measured with the CMOS sensor resulted in 4.88 ± 0.01 mm and agreed satisfactorily with the film-measured value (5.16 ± 0.04 mm), within 5.4%. At 10 MV, a 5.13 ± 0.01 mm field size was measured with the CMOS sensor compared with a value 5.25 ± 0.04 cm obtained from film measurement, resulting in a 2.3% difference. It can be seen that CMOS sensor-measured profiles are narrower than those measured with film. It appears the CMOS sensor slightly sharpens the field size at both energies (by 0.28 ± 0.05 mm and 0.12 ± 0.05 mm at 6 MV and 10 MV, respectively). The reason for the dicrepancy between field sizes may be due to the variation of transport properties between silicon and water, which is energy dependent (Beddar et al 1994). Nevertheless, as described above the effect is very small. It is important to note that this sharpening effect was not observed from the MC simulation in silicon (see table 2). Perhaps, a small mismatch between the Monte Carlo modelling and the actual jaw position of our linear accelerator is likely to cause the discrepancy, assuming GEANT4 describes accurately radiation transport in silicon. However, this was not investigated in this work. 4392
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(a)
(b)
Figure 8. Comparison of the 0.5 × 0.5 cm2 measured profiles using film and the CMOS sensor at 10 cm deep. (a) Profiles for the 6 MV and (b) 10 MV beam. Table 2. Penumbrae and field sizes for the 0.5 × 0.5 cm2 field measured with the
CMOS sensor and compared with film and MC simulation in silicon. Penumbra (L) and (R) indicate penumbrae measured on the left and right side from the central axis.
Field size Penumbra (L) Penumbra (R)
MC silicon (±0.01 mm)
Actual sensor (±0.01 mm)
Film (±0.04 mm)
5.12 1.92 1.88
4.88 1.82 1.85
5.16 1.86 1.78
Note: Uncertainties are indicated in parenthesis.
The 20%–80% penumbra widths mesured with film and the CMOS sensor for the 6 MV beam are also given in table 2. There are small variations between penumbrae measured on the left and right sides from the central axis. The MC-simulated profile in silicon shows a 2.1% difference, compared with a 4.4% for film. If left-measured penumbrae are compared, it is seen that CMOS sensor-measured penumbra is narrower just by 2.2% respect to film, but comparable within the quoted uncertainties. For the 10 MV beam, the values 2.25 ± 0.04 mm and 2.21 ± 0.01 mm were obtained for film and sensor, respectively, resulting in an agreement within 1.8%. The increase of field size and penumbra width measured at 10 MV compared to 6 MV, using both detectors, is presumably due to the larger lateral range of the secondary electrons with higher energy. 3.4. Tissue-phantom ratios
Tissue-phantom ratios for a 10 × 10 cm2 field at 6 MV and 10 MV energies, normalized to 10 cm depth are given in table 3. Differences between ionization chamber and sensor measurements at both energies are within 0.3 to 0.8% for the 6 MV beam, and within 0.2 to 0.8% for the 10 MV beam, showing that for this field the performace of the CMOS sensor to measure TPRs is comparable to chamber. Calculated TPRs for the 0.5 × 0.5 cm2 field are compared with sensor measurements in table 4, showing a maximum difference of −1.5%, for the 20 cm square field, relative to the MC-simulated values. 4393
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Table 3. Comparison of tissue phantom ratios (TPRs) for the 6 MV beam measured with the CMOS sensor and a Farmer ionization chamber (IC) in Solid Water for 10 × 10 cm2 field. The data were normalized to 10 cm depth and the detectors placed at 100 cm SAD.
6 MV beam
10 MV beam
Depth (cm)
TPR Sensor
Diff. TPR IC (%)
TPR Sensor
Diff. TPR IC (%)
5 10 15 20 25
1.191 ± 0.005 1.000 ± 0.005 0.815 ± 0.004 0.660 ± 0.002 0.540 ± 0.002
1.188 1.000 0.819 0.665 0.538
1.142 ± 0.002 1.000 ± 0.001 0.869 ± 0.006 0.739 ± 0.005 0.625 ± 0.001
1.138 1.000 0.862 0.735 0.626
0.3 0.0 − 0.5 − 0.8 0.4
0.4 0.0 0.8 0.5 − 0.2
Note: The error on the IC-measured TPRs are within ± 0.2%. The difference between TPRs is expressed as a percentage of the IC value. Table 4. Comparison of tissue phantom ratios (TPRs) for the 6 MV beam measured with the CMOS sensor in Solid Water and calculated with Monte Carlo simulation in water for the 0.5 × 0.5 cm2 field.
Depth (cm)
TPR Sensor
TPR MC
Diff. (%)
5 10 15 20 25
1.302 ± 0.003 1.000 ± 0.003 0.780 ± 0.003 0.607 ± 0.002 0.481 ± 0.001
1.299 ± 0.014 1.000 ± 0.009 0.771 ± 0.007 0.616 ± 0.007 0.477 ± 0.005
0.2 0.0 1.2 − 1.5 0.8
Note: The difference between TPRs is expressed as a percentage of the MC-simulated value.
3.5. Output factors
Figure 9 shows output factors at 10 cm deep for field sizes from 25 × 25 cm2 down to 0.5 × 0.5 cm2 for 6 MV energy beam, normalized to 10 × 10 cm2 and 5 × 5 cm2 reference fields. The 5 cm field was chosen as an intermediate reference field to interpret output factors for the smaller fields, while the 10 cm reference field normalization allows us to interpret output factors measured for the larger fields. A marked field size dependence is observed from figure 9(a). The CMOS sensor shows an increasing response compared to IC measurements for field sizes between 15 cm and 25 cm. The variation increases from 0.4% for the 15 cm field up to 1.5% for the 25 cm field, where the percentage difference is quoted with respect to IC results. This field size dependence has also been reported by others (Laub and Wong 2003, Yorke et al 2005, Scott et al 2012, Benmakhlouf et al 2014) and it is atributed to the difference in atomic number and density of the detector material compared to water. Figure 9(b), which was normalized to the 5 cm field, shows a partial over response of the CMOS sensor compared to MC simulations in water, as the field becomes smaller. A difference of around 2.9% exists between the simulated and measured output factors, with the exception of the small 0.5 cm field, where a difference of 6.3% was found. This result is, however, expected as it has been reported earlier by Scott et al (2008) at a 15 MV energy beam. This result is further supported by figures 9(c) and (d), where dose values for output factors calculation have been obtained from a fifth order polynomial fitting to the depth dose curves. A better agreement can be seen at all field sizes showing a maximum difference of 4394
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Figure 9. Comparison of MC-simulated, IC and CMOS sensor-measured output
factors normalized to (a) 10 × 10 cm2 field and (b) 5 × 5 cm2 field, where dose values for output factors calculation were obtained from dose scored in a voxel. In (c) and (d) output factors are calculated from dose values obtained from a fifth order polynomial fitting to depth dose curves between 5 cm to 20 cm deep. Measurement error bars are smaller than symbols.
1.8% (compared to MC results), however at the smallest field size a marked difference of almost 4% is found. 4. Discussion The purpose of this work was to assess the performance of CMOS active pixel sensors for small field measurements. As CMOS imagers suffer from several sources of noise (Tian et al 2001), an optical calibration was performance to quantify them. Photon transfer curves were used to accomplish noise quantification as shown in figure 4. The total noise was found to be about 2.2% of the signal, with FPN the dominant noise source. However, FPN can be accurately corrected for by applying flat-fielding techniques (Janesick 2007). This can remove FPN and achieve the shot noise limit, which as can be seen in figure 5 account for less than 0.5% of the total noise, thereby significantly improving signal to noise ratio. The accuracy of penumbra and beam profile measurement is crucial for the overall success of a treatment. Volume averaging and, consequently, broadening of penumbra is caused by the limited spatial resolution of detectors employed to measure beam profiles. In this respect, 4395
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beam profiles measured with our CMOS sensor and compared with film in figures 8(a) and (b) are in good agreement. The penumbra widths agree to within 2.2 and 1.8% for 6 MV and 10 MV, respectively. The good agreement observed for penumbra measurement with the CMOS sensor supports the fact that CMOS sensors can overcome volume averaging effects as reported for diodes (Scott et al 2008, Scott et al 2009). Although the differences found for field sizes measured with the CMOS sensor and compared with film were relatively large at 6 MV and 10 MV (5.4% and 2.3%, respectively), the results obtained are nevertheless encouraging. The small size and thickness of the pixel provide a resolution comparable to film. As pixels can be considered as individual detector elements, it makes it possible to image, in two dimensions, the radiation field by a single measurement and overcome limited resolution and possitioning errors of several detectors (Paskalev et al 2003, Pappas et al 2008). The TPRs measured with the CMOS sensor were in good agreement with those measured with the ionization chamber and within 0.8%. The comparison between measured and simulated TPRs for the 0.5 cm square field agreed to within 1.5%. The variation with depth in phantom appears to be insignificant at 6 MV. As expected, the relatively high over-response of silicon in the low-energy range, observed from the x-ray silicon cross section compared to water has little effect on small field measurements. Similarly, the relatively low energy dependence due to the small variation of the mass collision stopping power ratios of water to silicon (Heydarian et al 1996, Scott et al 2008) in the MV energy range, supports the results obtained. From results presented in figure 9 it is seen that output factor measurements with CMOS sensors are feasible. CMOS sensor results agreed well with a Farmer ionization chamber for field sizes between 20 and 4 cm square, showing a deviation smaller than 2% for the energy beams investigated. However, because of the over response expected for silicon detectors to the low-energy photon component of the spectrum (Benmakhlouf et al 2014), which is present in larger fields, small corrections must be performed before using CMOS sensors for OF measurements at larger field. As demonstrated, the correction increases with field size up to 1.5%, but it is likely to increase more for larger field sizes not investigated in this work. For smaller fields the agreement with Monte Carlo simulation results is encouraging, particularly because charged particle disequilibrium is present at such fields (Alfonso et al 2008). Furthermore, small-field output factor measurements with CMOS sensors are not likely to be affected as ionization chambers. Scott et al (2012) found up to 16% difference between doses calculated from voxels of same dimension made of water and air. Manolopoulos et al (2009) also found with significant discrepancies reaching a maximum of around 12% with decreasing collimator size, beetween a silicon detector and a PinPoint chamber. Charles et al (2014) showed that output factors measured with ionization chambers are more affected than detectors of higher density for fields smaller than 15 mm square. Similarly, they found that a 1 mm detector possitioning error caused a nearly 7% error in output factor measurement, which is overcome as output factor measurements can be performed across the sensor array. However, the large deviations encountered between simulated and measured output factors for the 0.5 cm field (up tp 6.3% for the 6 MV beam), at first sight, limits the capability with which CMOS sensors can accurately measure output factors. We noted, however, that the influence of the treatment head modelling, in terms of electron spot size and the incident electron energy have been shown to affect output correction factors (Scott et al 2009). The modelled incident electron energy in the target by Hedin et al (2010) was 5.7 MeV and the assumption of a Gaussian spatial distribution with a FWHM of 0.1 cm. These parameters as well as modelling of source occlusion, indeed, determine the accurate description of the radiation beam (Scott et al 2008). Therefore, we conclude that this larg deviation is associated to the linac modelling rather than the CMOS sensor. 4396
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5. Conclusions Since the introduction of the camera-on-a-chip imaging concept by Fossum (1997), CMOS imaging sensors have received much more attention for scientific applications. CMOS active pixel sensors are expected to play a major role in medical physics, therefore an important aim of this investigation was to determine the feasibility of CMOS sensor technology as an alternative in small-field dosimetry. The results of this work have shown for the first time the clinical potential of CMOS active pixel sensors for small-field measurements. CMOS sensors offer high spatial resolution, speed and sensitivity to measure dose under conditions where ionization chambers and even small silicon diodes present practical difficulties. It was found that CMOS sensors can accurately measure beam parameters. The agreement with film measurement and Monte Carlo simulations was within clinical acceptance. Experimental measurements showed that CMOS sensors provide a spatial response that is suitable for small field measurements. It was found that at the energies and the small field investigated in this work, the off-axis variations of the sensor response across the field are small and do not limit beam profile and penumbra measurements. The dependence of the Vanilla response with depth was also assessed by TPR measurements. Experimental and Monte Carlo results showed that the response of the sensor agrees to within 1.0% when compared with ionizations chambers. These results are encouraging and show that CMOS active pixel sensors have the potential to attract the interest for dosimetric applications in radiation therapy. Acknowledgments We would like to thank M A Cortés-Giraldo for his assistance to read the phase-space files used in this work, V Rompokos from UCLH, and R Chakarova for helpful email discussions regarding the IAEA phase-space files. Francisco Jiménez-Spang was sponsored by Programa Nacional de Investigadores 2005-2010 IFARHU-SENACYT of the Republic of Panama. References Alfonso R et al 2008 A new formalism for reference dosimetry of small and nonstandard fields Med. Phys. 35 5179–86 Beddar A S, Mason D J and O'Brien P F 1994 Absorbed dose perturbation caused by diodes for small field photon dosimetry Med. Phys. 21 1075–9 Benmakhlouf H, Sempau J and Andreo P 2014 Output correction factors for nine small field detectors in 6 MV radiation therapy photon beams: a PENELOPE Monte Carlo study Med. Phys. 41 041711-1 –041711-12 Bigas M, Cabruja E, Forest J and Salvi J 2006 Review of CMOS image sensors Microelectron. J. 37 433–51 Blue A et al 2007 Characterisation of Vanilla: a novel active pixel sensor for radiation detection Nucl. Inst. Methods A 591 287–90 Bohndiek S E, Arvanitis C D, Royle G J, Speller R D, Clark A T, Crooks J P, Prydderch M L, Turchetta R, Blue A and O'Shea V 2007 Characterization studies of two novel active pixel sensors Opt. Eng. 46 124003 Bohndiek S E et al 2008 Comparison of methods for estimating the conversion gain of CMOS active pixel sensors IEEE Sensors 10 1734–44 Charles P H, Cranmer-Sargison G, Thwaites D I, Crowe S B, Kairn T, Knight R T, Kenny J, Langton C M and Trapp J V 2014 A practical and theoretical definition of very small field size for radiotherapy output factor measurements Med. Phys. 41 041707 4397
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Das I J, Ding G X and Ahnesjö A 2008 Small fields: nonequilibrium radiation dosimetry Med. Phys. 35 206–15 Das I J, Downes M B, Kassaee A and Tochner Z 2000 Choice of radiation detector in dosimetry of stereotactic radiosurgery-radiotherapy J. Radiosurg. 3 177–86 Duggan D M and Coffey C W 1998 Small photon field dosimetry for stereotactic radiosurgery Med. Dosim. 23 153–9 Elles S, Ivanchenko V N, Maire M and Urban L 2008 Geant4 Fano cavity test: where are we? J. Phys.: Conf. Ser. 102 012009 Fossum E R 1997 CMOS image sensors: electronic camera-on-a-chip IEEE Trans. Electron Devices 44 1689–98 Hedin E, Bäck A, Swanpalmer J and Chakarova R 2010 Monte Carlo simulation of linear accelerator Varian Clinac iX [online] (www-nds.iaea.org/phsp/photon1/VarianClinaciX_6MV_PHSPdoc_ Gothenburg.pdf) Heydarian M, Hoban P W and Beddoe A H 1996 A comparison of dosimetry techniques in stereotactic radiosurgery Phys. Med. Biol. 41 93–110 Tian H, Fowler B and El Gamal A 2001 Analysis of temporal noise in CMOS photodiode active pixel sensor IEEE J. Solid-State Circuits 36 92–101 Janesick J 2007 Photon Transfer DN → λ 1st edn (Bellingham, WA: SPIE Optical Engineering Press) p 21 Jang J, Kang Y-N, Shin H-J, Seo J-H, Kim M-C, Lee D-J and Kwong S-I 2011 Measurement of beam data for small radiosurgical fields: comparison of CyberKnife multi-sites in Korea Prog. Nucl. Sci. Technol. 1 537–40 Kleinfelder S, Bichsel H and Bieser F et al 2002 Integrated x-ray and charged particle active pixel CMOS sensor arrays using an epitaxial silicon sensitive region [online] (http://publications.lbl. gov/islandora/object/ir%3A120171/datastream/pdf/view) Laub W U and Wong T 2003 The volume effect of detectors in the dosimetry of small fields used in IMRT Med. Phys. 30 341–7 Manolopoulos S, Wojnecki C, Hugtenburg R, Jaafar Sidek M A, Chalmers G, Heyes G and Green S 2009 Small field measurements with a novel silicon position sensitive diode array Phys. Med. Biol. 54 485–95 Martens C, De Wagter C and De Neve W 2000 The value of the PinPoint ion chamber for characterization of small field segments used in intensity-modulated radiotherapy Phys. Med. Biol. 45 2519–30 McKerracher C and Thwaites D I 1999 Assessment of new small-field detectors against standard-field detectors for practical stereotactic beam data acquisition Phys. Med. Biol. 44 2143–60 Pappas E et al 2008 Small SRS photon field profile dosimetry performed using a PinPoint air ion chamber, a diamond detector, a novel silicon-diode array (DOSI), and polymer gel dosimetry. Analysis and intercomparison Med. Phys. 35 4640–8 Paskalev K A, Seuntjens J P, Patrocinio H J and Podgorsak E B 2003 Physical aspects of dynamic stereotactic radiosurgery with very small photon beams (1.5 and 3 mm in diameter) Med. Phys. 30 111–8 Sauer A and Wilbert J 2007 Measurement of output factors for small photon beams Med. Phys. 34 1983–8 Scott A J, Nahum A and Fenwick J D 2008 Using a Monte Carlo model to predict dosimetric properties of small radiotherapy photon fields Med. Phys. 35 4671–84 Scott A J D, Nahum A E and Fenwick J D 2009 Monte Carlo modeling of small photon fields: quantifying the impact of focal spot size on source occlusion and output factors, and exploring miniphantom design for small-field measurements Med. Phys. 36 3132–44 Scott A J, Kumar S, Nahum A and Fenwick J D 2012 Characterizing the influence of detector density on dosimeter response in non-equilibrium small photon fields Phys. Med. Biol. 57 4461–76 Sibata C H, Mota H C, Beddar A S, Higgins P D and Shin K H 1991 Influence of detector size in photon beam profile measurements Phys. Med. Biol. 36 621–31 Turchetta R et al 2001 A monolithic active pixel sensor for charged particle tracking and imaging using standard VLSI CMOS technology Nucl. Inst. Methods Phys. Res. A 458 677–89 Turchetta R, French M, Manolopoulos S, Tyndel M, Allport P, Bates R, O'Shea V, Hall G and Raymond M 2003 Monolithic active pixel sensors (MAPS) in a VLSI CMOS technology Nucl. Inst. Methods Phys. Res. A 501 251–9 Yorke E et al 2005 Diode in vivo dosimetry for patients receiving external beam radiation therapy AAPM Report No 87
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Photon small-field measurements with a CMOS active pixel sensor
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Institute of Physics and Engineering in Medicine Phys. Med. Biol. 60 (2015) 4383–4398
Physics in Medicine & Biology doi:10.1088/0031-9155/60/11/4383
Photon small-field measurements with a CMOS active pixel sensor F Jiménez Spang1, I Rosenberg2, E Hedin3 and G Royle1 1
Department of Medical Physics and Bioengineering, University College London, Gower Street, London WC1E 6BT, UK 2 UCLH NHS Foundation Trust, 250 Euston Road, London NW1 2PQ, UK 3 Department of Radiation Physics, Sahlgrenska Universitetssjukhuset, 41345 Göteborg, Sweden E-mail: [email protected] Received 3 February 2015, revised 27 March 2015 Accepted for publication 14 April 2015 Published 18 May 2015 Abstract
In this work the dosimetric performance of CMOS active pixel sensors for the measurement of small photon beams is presented. The detector used consisted of an array of 520 × 520 pixels on a 25 µm pitch. Dosimetric parameters measured with this sensor were compared with data collected with an ionization chamber, a film detector and GEANT4 Monte Carlo simulations. The sensor performance for beam profiles measurements was evaluated for field sizes of 0.5 × 0.5 cm2. The high spatial resolution achieved with this sensor allowed the accurate measurement of profiles, beam penumbrae and field size under lateral electronic disequilibrium. Field size and penumbrae agreed within 5.4% and 2.2% respectively with film measurements. Agreements with ionization chambers better than 1.0% were obtained when measuring tissue-phantom ratios. Output factor measurements were in good agreement with ionization chamber and Monte Carlo simulation. The data obtained from this imaging sensor can be easily analyzed to extract dosimetric information. The results presented in this work are promising for the development and implementation of CMOS active pixel sensors for dosimetry applications. Keywords: CMOS active pixel sensors, small-field dosimetry, Monte Carlo simulation, photon transfer curves, geant4 (Some figures may appear in colour only in the online journal) 1. Introduction As the radiation field becomes smaller techniques used for dosimetry of standard-size radiation fields are no longer valid (Das et al 2008). Loss of charged particle equilibrium and 0031-9155/15/114383+16$33.00 © 2015 Institute of Physics and Engineering in Medicine Printed in the UK
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volume averaging cause beam calibration to become inaccurate when the detector size is comparable to the radiation field, making the determination of dose questionable at best (Sibata et al 1991, Duggan and Coffey 1998). Miscalculation of dose due to inappropriate detector size can have clinical consequences for the outcome of treatments (Laub and Wong 2003). The use of dosimeters with high spatial resolution is therefore required (Das et al 2000, Jang et al 2011). Even though ionization chambers are the gold standard for radiation dosimetry, they present limitations to accurately measure small-field dosimetric parameters (McKerracher and Thwaites 1999, Martens et al 2000, Laub and Wong 2003). Several detectors have been proposed for small-field measurements. McKerracher and Thwaites (1999) found that no single detector was ideal for measurements of the small fields investigated in their study. Laub and Wong (2003) studied the effect of detector size for small fields using a p-type silicon diode, a 3 mm3 diamond detector and a set of ionization chambers and film. They found significant discrepancies for profile and output factor measurements of small fields and concluded that the limited spatial resolution of the detectors leads to inaccuracies in the commissioning of IMRT. Sauer and Wilbert (2007) investigated several detectors for small-field output factor measurements and calculated corrections for solid state detectors. Pappas et al (2008) compared several detectors with a silicon-diode array and found that detector size and detector composition, as well as positioning difficulties are the main problems related to small field profile measurements. More recently, Monte Carlo techniques have been used to calculate correction factors in small fields. Scott et al (2012) calculated density-correction factors for ion chambers and solid-state detectors. They found that changes in those factors with field size were due to differences between detector materials and water. Benmakhlouf et al (2014) use Monte Carlo simulations to calculate output correction factors of several detectors on a 6 MV beam. In this paper the application of CMOS active pixel sensors (CMOS APS) (Fossum 1997, Bigas et al 2006) for the dosimetry of small photon fields is presented. CMOS sensors have the advantage of very small pixel size and the capability to provide two-dimensional information and fast readout. CMOS APS are formed from an array of pixels. Each pixel is a radiation sensitive element with a photodiode, a capacitor and three transistors. CMOS sensors are described as active because they contain at least one active device per pixel, allowing the charge to be directly transferred from the pixel to the output by randomly addressing each pixel. A row-based readout architecture provides random access to pixels avoiding charge transfer over long distances as occurred in CCD readout technology. This makes CMOS sensors more suitable for dosimetry applications. The device used in this work, Vanilla (Blue et al 2007), is a 25 µm pixel pitch sensor which provides sufficient spatial resolution for small field measurements. Beam profiles and tissue phantom ratios were measured and compared with ionization chamber measurements and Monte Carlo simulations. It is demonstrated that CMOS APS have the potential to measure dosimetric parameters of small-photon beams accurately and overcome the main problems related to small field measurements, in particular positioning difficulties and limited high spatial resolution. 2. Materials and methods 2.1. Linear accelerator
A clinical linear accelerator model Varian 2100CD (Varian, Palo Alto, CA) was used for all measurements. The Varian 2100CD produces x-ray beams with photon energies of 6 and 10 MV. Square fields from 0.5 × 0.5 cm2 to 25 × 25 cm2 at a source-to-axis distance (SAD) of 4384
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Figure 1. Architecture of the Vanilla sensor (left) and pixel (right).
100 cm were produced using the collimator jaws. The Monitor Units (MU) were calibrated to deliver 1 cGy MU−1 at 95 cm source-to-surface distance (SSD) and a depth of 5 cm in water for a 10 × 10 cm2 field. 2.2. Detector system
The sensor and the pixel architectures are shown in figure 1. The sensor has two operation modes. In the digital mode, the analog to digital conversion of the voltage inside the pixel is performed by the on-chip ADCs. There are 130 ADCs on-chip to perform a 12-bit successive approximation conversion. In the analog mode the voltage signal in the pixel is converted using a 12-bit ADC on an expansion board. Image acquisition and control of the sensor were performed through the MI-3 OptoDAq system. This system was based on a Memec Virtex-II Pro™ 20FF1152 FPGA development board which generated the required control signal for the sensor. Further details can be found in Blue et al (2007). Three transistors and a photodiode (PD) are present inside the pixel. The transistor MRST is used to reset the pixel, MIN is the buffer and MSEL is used to select the readout of the pixel. After ionizing radiation interacts in the pixel sensitive volume, the generated electrons are collected by the diodes implanted into the pixel volume due to charge diffusion (Turchetta et al 2001, Kleinfelder et al 2002). The collected charge is integrated by the action of a capacitor in each pixel. This charge is then transferred to the column output through the charge amplifier by clocking the row selectors sequentially allowing the full image to be progressively read out from the pixels. The column output is then serially transferred by a readout register to an analog-to-digital converter to finally form the image which is analyzed to extract dosimetric information. 2.3. Sensor calibration
The sensor was optically calibrated through photon transfer (PT) curves (Bohndiek et al 2008) to convert ADC outputs to absolute units (e−) through the ADC sensor conversion gain 4385
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Figure 2. Schematic of the experimental setup used for the sensor characterization.
KADC(e−/DN), where DN represents computer digital number units. This calibration also helped us correct the intrinsic nonlinearities present in CMOS imagers (Janesick 2007). By characterizing the sensor signal in terms of electron units a direct connection with dosimetry can be achieved. In addition, a full determination and quantification of sources of noise can be obtained from the same analysis. The sensor was placed inside a metallic black box (figure 2) and stimulated by a 520 nm narrow-band light emitter diode (LumiLED) coupled with two white diffusion sheets (Lee Filters, white 129) with 87% attenuation. A lens was placed in front of the LED to focus light intensity across the sensor surface. Light intensity was varied by changing the voltage across the LED to cover the dynamic range of the sensor. The voltage was uniformly varied from 2.16 V up to 19.68 V to achieve sensor saturation using steps of 0.08 V. From the collected data the sensitivity K(e−/DN) was calculated as S (DN) K (e− /DN) = (1) σS (DN)2 − σR(DN)2
where S (DN) is the signal in digital numbers (DN), σR(DN) is the read noise, and σS(DN) is the total noise. The difference σS(DN)2 − σR(DN)2 is the shot noise. The total noise is found from ⎧ ⎫1/2 S (DN) 2 ⎬ [ (DN) ] P S σS (DN) = ⎨σR(DN)2 + + (2) N ⎩ ⎭ K (e− /DN)
where the last term is the fixed pattern noise (FPN) and PN is called the quality factor, which is approximately 0.02 for CMOS and CCD sensors (Janesick 2007). For equation (2) to be useful, shot noise must be isolated. By subtracting two consecutive frames at the same illumination level the FPN is removed. Read noise is found from the intercept in the PT curve and subtracted from the remaining term in equation (2). Once shot noise is isolated, the sensor parameters can be determined. The set of equations used to generate PT data are given below: 1 S¯k = ∑ Sik, j. (3) LM i, j 1 S¯ = (S¯A + S¯B ) − S¯D. (4) 2 4386
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1 σS2 = ∑ [(SiA, j − S¯A) − (SiB, j − S¯B )]2 . (5) 2(N − 1) i, j
where S¯k is the mean frame, L and M are the number of rows and columns in the frame, respectively, S¯A and S¯B are two consecutive frames that must be subtracted to remove fixed pattern noise, and σS2 is the signal variance. The indexes of summation i and j go from 0 to L − 1 and 0 to M − 1, respectively. For the correction of the sensor nonlinearities photon flux measurements had to be accurately determined. A calibrated photodiode (Hamamatsu S1336-5BQ) was placed at the same position of the sensor after image acquisition. The output current, which is proportional to the photon flux input signal, was measured using a Keithley 237 High Voltage Source-Measure Unit. Over a hundred measures were averaged to obtain the output current that corresponded to each illumination level to calculate the total number of incident photons per pixel during the sensor integration time. This data was then applied to the data collected from equations (3) to (5) and a corrected conversion gain (SADC(e−/DN)) was calculated from KADC(e−/DN), the signal and the incident photons per pixel. To quantify how much x-ray shot noise limits sensor performance, signal-to-noise ratio (SNR) was calculated from SNR =
S
σTOTAL (6) S = 2 + ηiS + (PN S )2]1/2 [σREAD
where ηi is the quantum yield and S the signal. From equation (6) it can be seen that SNR within the shot noise regime is proportional to the square root of signal. Shot noise limits the signal-to-noise performance when detected signals are large, which represents a fundamental limit for imaging sensors. 2.4. Measurements
Dosimetric parameters such as beam profiles, tissue-phantom ratios (TPRs) and output factors were measured with the Vanilla sensor at 6 and 10 MV photon energies and compared with ionization chamber, film measurements and Monte Carlo (MC) simulations. To prevent sensor saturation, the dose rate of the linear accelerator was restricted throughout to 100 MU min−1 and the sensor was run at 55 frames per second with an integration time of 18 ms. Before measurements a dark image was averaged over 100 frames to correct for the offset signal. The offset signal comprised mainly read noise, but also any stimulus input signal present during measurements. This dark image was then subtracted from all measurements. For all measurements the sensor was embedded in a slab of Perspex of size 30 × 30 × 1 cm3 as shown in figure 3. Slabs of Solid Water (SW) totalling 4 cm thick were placed on top to obtain a total build-up of 5 cm, to eliminate electron contamination. A SW slab of 10 cm was used for backscatter. 2.4.1. Beam profiles. Beam profiles for 6 and 10 MV photon beams with 0.5 × 0.5 cm2 fields
were imaged with the Vanilla sensor in SW. Profiles were also measured with radiographic X-OMAT V film and MC simulations for comparison. A Vidar film digitizer (VXR-16, Vidar Systems Corp., Herndon, VA) was used to scan the film. The film scanner was operated with a resolution of 300 dpi and a depth of 12 bits. 4387
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Figure 3. Experimental setup for dosimetric parameter measurements.
The sensor was placed in SW slabs at depths from 5 to 25 cm, but at a constant source to detector distance of 100 cm. A set of 100 frames were averaged to get a final image which was then analyzed using Matlab and ImageJ to generate the beam profiles. The small 0.5 × 0.5 cm2 beam profile was measured with film and the CMOS sensor after measuring the output factor for the same field, without moving the collimators to avoid collimator positional erros. 2.4.2. Tissue-phantom ratios (TPRs). TPRs are defined as the ratio of the signal at a given depth to a reference depth of 10 cm, with a field size of 10 × 10 cm2 at a constant SAD. The signal was integrated in a region of interest (ROI) of 1 mm2 at the centre of the sensor array. The mean number of electrons was calculated by converting the average signal in the ROI to electrons through the ADC signal sensitivity. TPRs were also measured using a Farmer ionization chamber for comparison with the CMOS sensor results. 2.4.3. Output factors. Output factors measured with the sensor were calculated as the ratio of the average pixel signal over a ROI of 40 × 40 pixels to a reference field of 10 × 10 cm2, at 10 cm deep at the isocentre in the phantom. The linear accelerator was operated at 100 MU min−1 for sensor measurements to prevent sensor saturation and at 600 MU min−1 when measuring with the Farmer ionization chamber. Ionization chamber measurements were done for fields between 4 × 4 cm2 and 25 × 25 cm2. Comparisons were done with simulated OFs obtained from the work by Hedin et al (2010) at SSD 90 cm and SAD 100 cm. Dose values for OF were calculated in two different ways; directly from the energy deposited in a voxel and from dose values obtained from a fifth order polynomial fitted to the depth dose curves for depths between 5 cm and 20 cm. 2.4.4. Monte Carlo simulations Phase-space files. As no appropriate detectors for small field dosimetry was in use at the
Radiotherapy Department at UCLH at the moment of this work, Monte Carlo simulations were performed to compare a set of TPRs measured with the sensor to MC-simulated TPRs for a small 6 MV 0.5 × 0.5 cm2 beam. The simulations were performed using the GEANT4 9.2 4388
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Table 1. Composition and thickness of the layers simulated in the model of the sensor.
Layer
Composition
Thickness (μm)
Pasivation Silicon dioxide Aluminum Epitaxiala Substrate PCBb
SiNO3 SiO2 Al Si Si SiO2 (70%) C15O2H16 (23%) C3H6O (7%) Cu
1 4 1 14 500 1664
Copper in PCB
35
Note:a Sensitive volume. b Printed Circuit Board.
implementation of PENELOPE, with all electron transport parameters optimized as described in Elles et al (2008). The dose values were scored in cylinders of radius 0.05 cm and height 0.3 cm at the central axis of a water phantom of dimensions 30 × 30 × 20 cm3. Simulations were repeated three times to estimate uncertainties. The incident spectrum was obtained from a collection of 6 MV phasespace files of a Varian linear accelerator Clinac iX published on the IAEA NAPC Nuclear Data Section web site (Hedin et al 2010), and selected as representative of our Varian 2100CD. The linac MC modelling was based on 5.7 MeV monoenergetic electrons impinging on the target normally with a Gaussian spatial distribution of 0.1 cm. To determine the validity of this comparison, quality indexes (TPR10 20) of both the Varian 2100CD and the phase-space file were compared. Additionally, a 0.5 × 0.5 cm2 field was simulated in water and compared with a filmmeasured profile at similar conditions. This simulation setup consisted of an array of 52 × 52 voxels of area 0.025 × 0.025 cm2 and 0.1 cm thick at 10 cm deep at the origin of the water phantom. The uncertainty in the field size was estimated as half of the off-axis distance from the origin to the voxel centre. Sensor simulation. The sensor was precisely modelled using GEANT4 to score a dose beam profile of the small 6 MV 0.5 × 0.5 cm2 field in the sensor sensitive layer. This profile field size was then compared with actual measurements. The sensor was modelled as a layered detector consisting of six different layers. Table 1 shows the composition and thickness of the layers used in the Monte Carlo model according to information provided by the designers of the detector. The sensitive layer of the detector was divided in voxels of area 25 × 25 µm2 and height 14 µm to mimic the pixel pitch of the actual sensor. Energy deposited was scored in 520 × 520 voxels in the sensitive layer. As the sensitive volume of the detector was very thin (14 µm), we set the electron cut-off in this layer to 100 eV. In the Solid Water phantom the electron cut-off was set to a large value to stop the production of secondary electrons and allow a continuous-slowing-down energy deposition. This also reduced the simulation time.
3. Results 3.1. Sensor calibration
Figure 4(a) shows the PT curves with all sources of noise shown independently. The read noise, which is a signal-independet noise, was calculated from an analysis performed on 4389
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(a)
(b)
Figure 4. Photon transfer results: (a) photon transfer curve derived from measurements with the Vanilla sensor, (b) false signal versus the true signal based on SADC(e−/DN).
different regions of interest (ROIs) over the dark frames. A value σREAD = 2.63 ± 0.02 DN was estimated. From the raw data plotted in figure 4(a) it was noted that the shot noise curve deviates from the typical 0.5 slope on a Log–Log graph, indicating that the ADC sensitivity KADC(e−/DN) is dependent on signal level and therefore nonlinear. This sensitivity varies from 17.83 e−/DN to 23.04 e−/DN showing a maximum nonlinearity of 29%. The effect of this nonlinearity on the signal is shown in figure 4(b) where the false signal (calculated from KADC(e−/DN)) is compared with the true signal (corrected from SADC(e−/DN)). The new ADC signal sensitivity SADC(e−/DN) was found through a nonlinear compensation by using the incident photon flux on the pixel array to progressively correct the nonlinearity of the signals at higher levels, from the very first signal (Bohndiek et al 2008). From this procedure corrected PTC curves were generated, and additionally, all pixel values from all images were also corrected. For estimating read noise, KADC(e−/DN) at the very first signal level was used, resulting in σREAD = 47 ± 1e−. Figure 5 compares all sources of noise as a function of signal. For most of the dynamic range of the sensor the total noise represents about 2.2% of the signal. Note that FPN dominates at higher signal levels accounting for 2.0% of the signal. From the FPN curve the quality factor resulted in PN = 0.020 (2.0%), which allows us to express the FPN as FPN = 0.020 × S, where S is the signal. 3.2. Monte Carlo simulations Phase-space files. The first comparison made for the phase-space file validation was the
quality index of the machines (QI) or TPR20/10 measured for a 10 × 10 cm2 field. This comparison was made between the quality control data of four linear accelerators available at UCLH and MC simulations with the phase-space files. The average QI calculated with data from our four linear accelerators was 0.6644 ± 0.0015, which is in good agreement, within the statistical uncertainties, with the result obtained from the 6 MV phase-space file simulation, 0.6636 ± 0.0062. This is a good indication that the phase-space file produced a similar beam quality as the beams used in the measurements. Figure 6(a) compares the simulated beam profile in water and that measured with film for the 0.5 × 0.5 cm2 field at 10 cm deep. Field sizes calculated from the Monte Carlo-simulated small field and from the measured profile were in excellent agreement. From the Monte Carlo 4390
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Figure 5. Comparison of sources of noise plotted independently as function of signal.
Figure 6. Profiles for a 6 MV 0.5 × 0.5 cm2 field at 10 cm deep in phantom. (a)
Comparison of MC-simulated profile in water and film-measured profile in Solid Water, (b) comparison of MC-simulated profile in the sensitive layer of the sensor and measured with film in Solid Water.
simulation a value 5.1 ± 0.2 mm was obtained for field size. The corresponding field size measured with film was 5.10 ± 0.04 cm. This comparison shows an excellent match between the Monte Carlo beam model for the smallest field and the experimental beam of the Varian 2100CD. Sensor simulation. Figure 6(b) shows the simulated profile in silicon compared to the corresponding film-measured profile. Because of the low efficiency obtained during the simulation of this thin detector, the particles of the phase-space file were recycled 300 times. To reduce the statistical fluctuations, the beam profile was plotted by averaging (vertically) the dose deposited in 21 rows of pixels, from which 10 were above and below the central row of the detector array. The resulting profile was taken as representative of the dose profile in the central row. The profile was then smoothed using a Savitzky–Golay filter available in Matlab. 4391
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(a)
(b)
Figure 7. Beam profiles mesured in Solid Water with the CMOS sensor for a field size
0.5 × 0.5 cm2. The profiles were plotted from a single row of pixels across the sensor array, (a) 6 MV beam, (b) 10 MV beam.
A field size 5.12 ± 0.01 mm was obtained from the MC-simulated sensor, which agreed well with film (0.8%). Similarly, penumbra widths were in good agreement. The MC-simulated penumbra resulted in 1.92 ± 0.01 mm, compared with a film-measured penumbra of 1.86 ± 0.04 mm, which differed by 3.2%. From these results, it was determined that the phase-space file of the 0.5 × 0.5 cm2 field as well as the Monte Carlo modelling of the sensor were accurate for the comparisons presented in the following sections. 3.3. Beam profiles
Figure 7 shows the beam profiles measured with the CMOS sensor at different depths in SW. The ADC signal was converted to e− to correct for sensor nonlinearities. Profiles variations with depth and beam energy can be noted by comparing the graphs. Pixel response non-uniformity and fixed pattern noise effect can be observed more clearly from the 10 MV profiles, where the same fixed pattern on the profiles were reproduced at all depths. This can, however, be corrected by applying a smoothing filter on the data. Figure 8 comparesthe beam profiles for a 0.5 × 0.5 cm2 field measured with the CMOS sensor and film at 10 cm deep. Their agreement was evaluated by comparing the 20%–80% penumbra width and field size (full width at half maximum, FWHM). As shown in table 2, the field size of the small 6 MV beam measured with the CMOS sensor resulted in 4.88 ± 0.01 mm and agreed satisfactorily with the film-measured value (5.16 ± 0.04 mm), within 5.4%. At 10 MV, a 5.13 ± 0.01 mm field size was measured with the CMOS sensor compared with a value 5.25 ± 0.04 cm obtained from film measurement, resulting in a 2.3% difference. It can be seen that CMOS sensor-measured profiles are narrower than those measured with film. It appears the CMOS sensor slightly sharpens the field size at both energies (by 0.28 ± 0.05 mm and 0.12 ± 0.05 mm at 6 MV and 10 MV, respectively). The reason for the dicrepancy between field sizes may be due to the variation of transport properties between silicon and water, which is energy dependent (Beddar et al 1994). Nevertheless, as described above the effect is very small. It is important to note that this sharpening effect was not observed from the MC simulation in silicon (see table 2). Perhaps, a small mismatch between the Monte Carlo modelling and the actual jaw position of our linear accelerator is likely to cause the discrepancy, assuming GEANT4 describes accurately radiation transport in silicon. However, this was not investigated in this work. 4392
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(a)
(b)
Figure 8. Comparison of the 0.5 × 0.5 cm2 measured profiles using film and the CMOS sensor at 10 cm deep. (a) Profiles for the 6 MV and (b) 10 MV beam. Table 2. Penumbrae and field sizes for the 0.5 × 0.5 cm2 field measured with the
CMOS sensor and compared with film and MC simulation in silicon. Penumbra (L) and (R) indicate penumbrae measured on the left and right side from the central axis.
Field size Penumbra (L) Penumbra (R)
MC silicon (±0.01 mm)
Actual sensor (±0.01 mm)
Film (±0.04 mm)
5.12 1.92 1.88
4.88 1.82 1.85
5.16 1.86 1.78
Note: Uncertainties are indicated in parenthesis.
The 20%–80% penumbra widths mesured with film and the CMOS sensor for the 6 MV beam are also given in table 2. There are small variations between penumbrae measured on the left and right sides from the central axis. The MC-simulated profile in silicon shows a 2.1% difference, compared with a 4.4% for film. If left-measured penumbrae are compared, it is seen that CMOS sensor-measured penumbra is narrower just by 2.2% respect to film, but comparable within the quoted uncertainties. For the 10 MV beam, the values 2.25 ± 0.04 mm and 2.21 ± 0.01 mm were obtained for film and sensor, respectively, resulting in an agreement within 1.8%. The increase of field size and penumbra width measured at 10 MV compared to 6 MV, using both detectors, is presumably due to the larger lateral range of the secondary electrons with higher energy. 3.4. Tissue-phantom ratios
Tissue-phantom ratios for a 10 × 10 cm2 field at 6 MV and 10 MV energies, normalized to 10 cm depth are given in table 3. Differences between ionization chamber and sensor measurements at both energies are within 0.3 to 0.8% for the 6 MV beam, and within 0.2 to 0.8% for the 10 MV beam, showing that for this field the performace of the CMOS sensor to measure TPRs is comparable to chamber. Calculated TPRs for the 0.5 × 0.5 cm2 field are compared with sensor measurements in table 4, showing a maximum difference of −1.5%, for the 20 cm square field, relative to the MC-simulated values. 4393
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Table 3. Comparison of tissue phantom ratios (TPRs) for the 6 MV beam measured with the CMOS sensor and a Farmer ionization chamber (IC) in Solid Water for 10 × 10 cm2 field. The data were normalized to 10 cm depth and the detectors placed at 100 cm SAD.
6 MV beam
10 MV beam
Depth (cm)
TPR Sensor
Diff. TPR IC (%)
TPR Sensor
Diff. TPR IC (%)
5 10 15 20 25
1.191 ± 0.005 1.000 ± 0.005 0.815 ± 0.004 0.660 ± 0.002 0.540 ± 0.002
1.188 1.000 0.819 0.665 0.538
1.142 ± 0.002 1.000 ± 0.001 0.869 ± 0.006 0.739 ± 0.005 0.625 ± 0.001
1.138 1.000 0.862 0.735 0.626
0.3 0.0 − 0.5 − 0.8 0.4
0.4 0.0 0.8 0.5 − 0.2
Note: The error on the IC-measured TPRs are within ± 0.2%. The difference between TPRs is expressed as a percentage of the IC value. Table 4. Comparison of tissue phantom ratios (TPRs) for the 6 MV beam measured with the CMOS sensor in Solid Water and calculated with Monte Carlo simulation in water for the 0.5 × 0.5 cm2 field.
Depth (cm)
TPR Sensor
TPR MC
Diff. (%)
5 10 15 20 25
1.302 ± 0.003 1.000 ± 0.003 0.780 ± 0.003 0.607 ± 0.002 0.481 ± 0.001
1.299 ± 0.014 1.000 ± 0.009 0.771 ± 0.007 0.616 ± 0.007 0.477 ± 0.005
0.2 0.0 1.2 − 1.5 0.8
Note: The difference between TPRs is expressed as a percentage of the MC-simulated value.
3.5. Output factors
Figure 9 shows output factors at 10 cm deep for field sizes from 25 × 25 cm2 down to 0.5 × 0.5 cm2 for 6 MV energy beam, normalized to 10 × 10 cm2 and 5 × 5 cm2 reference fields. The 5 cm field was chosen as an intermediate reference field to interpret output factors for the smaller fields, while the 10 cm reference field normalization allows us to interpret output factors measured for the larger fields. A marked field size dependence is observed from figure 9(a). The CMOS sensor shows an increasing response compared to IC measurements for field sizes between 15 cm and 25 cm. The variation increases from 0.4% for the 15 cm field up to 1.5% for the 25 cm field, where the percentage difference is quoted with respect to IC results. This field size dependence has also been reported by others (Laub and Wong 2003, Yorke et al 2005, Scott et al 2012, Benmakhlouf et al 2014) and it is atributed to the difference in atomic number and density of the detector material compared to water. Figure 9(b), which was normalized to the 5 cm field, shows a partial over response of the CMOS sensor compared to MC simulations in water, as the field becomes smaller. A difference of around 2.9% exists between the simulated and measured output factors, with the exception of the small 0.5 cm field, where a difference of 6.3% was found. This result is, however, expected as it has been reported earlier by Scott et al (2008) at a 15 MV energy beam. This result is further supported by figures 9(c) and (d), where dose values for output factors calculation have been obtained from a fifth order polynomial fitting to the depth dose curves. A better agreement can be seen at all field sizes showing a maximum difference of 4394
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Figure 9. Comparison of MC-simulated, IC and CMOS sensor-measured output
factors normalized to (a) 10 × 10 cm2 field and (b) 5 × 5 cm2 field, where dose values for output factors calculation were obtained from dose scored in a voxel. In (c) and (d) output factors are calculated from dose values obtained from a fifth order polynomial fitting to depth dose curves between 5 cm to 20 cm deep. Measurement error bars are smaller than symbols.
1.8% (compared to MC results), however at the smallest field size a marked difference of almost 4% is found. 4. Discussion The purpose of this work was to assess the performance of CMOS active pixel sensors for small field measurements. As CMOS imagers suffer from several sources of noise (Tian et al 2001), an optical calibration was performance to quantify them. Photon transfer curves were used to accomplish noise quantification as shown in figure 4. The total noise was found to be about 2.2% of the signal, with FPN the dominant noise source. However, FPN can be accurately corrected for by applying flat-fielding techniques (Janesick 2007). This can remove FPN and achieve the shot noise limit, which as can be seen in figure 5 account for less than 0.5% of the total noise, thereby significantly improving signal to noise ratio. The accuracy of penumbra and beam profile measurement is crucial for the overall success of a treatment. Volume averaging and, consequently, broadening of penumbra is caused by the limited spatial resolution of detectors employed to measure beam profiles. In this respect, 4395
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beam profiles measured with our CMOS sensor and compared with film in figures 8(a) and (b) are in good agreement. The penumbra widths agree to within 2.2 and 1.8% for 6 MV and 10 MV, respectively. The good agreement observed for penumbra measurement with the CMOS sensor supports the fact that CMOS sensors can overcome volume averaging effects as reported for diodes (Scott et al 2008, Scott et al 2009). Although the differences found for field sizes measured with the CMOS sensor and compared with film were relatively large at 6 MV and 10 MV (5.4% and 2.3%, respectively), the results obtained are nevertheless encouraging. The small size and thickness of the pixel provide a resolution comparable to film. As pixels can be considered as individual detector elements, it makes it possible to image, in two dimensions, the radiation field by a single measurement and overcome limited resolution and possitioning errors of several detectors (Paskalev et al 2003, Pappas et al 2008). The TPRs measured with the CMOS sensor were in good agreement with those measured with the ionization chamber and within 0.8%. The comparison between measured and simulated TPRs for the 0.5 cm square field agreed to within 1.5%. The variation with depth in phantom appears to be insignificant at 6 MV. As expected, the relatively high over-response of silicon in the low-energy range, observed from the x-ray silicon cross section compared to water has little effect on small field measurements. Similarly, the relatively low energy dependence due to the small variation of the mass collision stopping power ratios of water to silicon (Heydarian et al 1996, Scott et al 2008) in the MV energy range, supports the results obtained. From results presented in figure 9 it is seen that output factor measurements with CMOS sensors are feasible. CMOS sensor results agreed well with a Farmer ionization chamber for field sizes between 20 and 4 cm square, showing a deviation smaller than 2% for the energy beams investigated. However, because of the over response expected for silicon detectors to the low-energy photon component of the spectrum (Benmakhlouf et al 2014), which is present in larger fields, small corrections must be performed before using CMOS sensors for OF measurements at larger field. As demonstrated, the correction increases with field size up to 1.5%, but it is likely to increase more for larger field sizes not investigated in this work. For smaller fields the agreement with Monte Carlo simulation results is encouraging, particularly because charged particle disequilibrium is present at such fields (Alfonso et al 2008). Furthermore, small-field output factor measurements with CMOS sensors are not likely to be affected as ionization chambers. Scott et al (2012) found up to 16% difference between doses calculated from voxels of same dimension made of water and air. Manolopoulos et al (2009) also found with significant discrepancies reaching a maximum of around 12% with decreasing collimator size, beetween a silicon detector and a PinPoint chamber. Charles et al (2014) showed that output factors measured with ionization chambers are more affected than detectors of higher density for fields smaller than 15 mm square. Similarly, they found that a 1 mm detector possitioning error caused a nearly 7% error in output factor measurement, which is overcome as output factor measurements can be performed across the sensor array. However, the large deviations encountered between simulated and measured output factors for the 0.5 cm field (up tp 6.3% for the 6 MV beam), at first sight, limits the capability with which CMOS sensors can accurately measure output factors. We noted, however, that the influence of the treatment head modelling, in terms of electron spot size and the incident electron energy have been shown to affect output correction factors (Scott et al 2009). The modelled incident electron energy in the target by Hedin et al (2010) was 5.7 MeV and the assumption of a Gaussian spatial distribution with a FWHM of 0.1 cm. These parameters as well as modelling of source occlusion, indeed, determine the accurate description of the radiation beam (Scott et al 2008). Therefore, we conclude that this larg deviation is associated to the linac modelling rather than the CMOS sensor. 4396
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5. Conclusions Since the introduction of the camera-on-a-chip imaging concept by Fossum (1997), CMOS imaging sensors have received much more attention for scientific applications. CMOS active pixel sensors are expected to play a major role in medical physics, therefore an important aim of this investigation was to determine the feasibility of CMOS sensor technology as an alternative in small-field dosimetry. The results of this work have shown for the first time the clinical potential of CMOS active pixel sensors for small-field measurements. CMOS sensors offer high spatial resolution, speed and sensitivity to measure dose under conditions where ionization chambers and even small silicon diodes present practical difficulties. It was found that CMOS sensors can accurately measure beam parameters. The agreement with film measurement and Monte Carlo simulations was within clinical acceptance. Experimental measurements showed that CMOS sensors provide a spatial response that is suitable for small field measurements. It was found that at the energies and the small field investigated in this work, the off-axis variations of the sensor response across the field are small and do not limit beam profile and penumbra measurements. The dependence of the Vanilla response with depth was also assessed by TPR measurements. Experimental and Monte Carlo results showed that the response of the sensor agrees to within 1.0% when compared with ionizations chambers. These results are encouraging and show that CMOS active pixel sensors have the potential to attract the interest for dosimetric applications in radiation therapy. Acknowledgments We would like to thank M A Cortés-Giraldo for his assistance to read the phase-space files used in this work, V Rompokos from UCLH, and R Chakarova for helpful email discussions regarding the IAEA phase-space files. Francisco Jiménez-Spang was sponsored by Programa Nacional de Investigadores 2005-2010 IFARHU-SENACYT of the Republic of Panama. References Alfonso R et al 2008 A new formalism for reference dosimetry of small and nonstandard fields Med. Phys. 35 5179–86 Beddar A S, Mason D J and O'Brien P F 1994 Absorbed dose perturbation caused by diodes for small field photon dosimetry Med. Phys. 21 1075–9 Benmakhlouf H, Sempau J and Andreo P 2014 Output correction factors for nine small field detectors in 6 MV radiation therapy photon beams: a PENELOPE Monte Carlo study Med. Phys. 41 041711-1 –041711-12 Bigas M, Cabruja E, Forest J and Salvi J 2006 Review of CMOS image sensors Microelectron. J. 37 433–51 Blue A et al 2007 Characterisation of Vanilla: a novel active pixel sensor for radiation detection Nucl. Inst. Methods A 591 287–90 Bohndiek S E, Arvanitis C D, Royle G J, Speller R D, Clark A T, Crooks J P, Prydderch M L, Turchetta R, Blue A and O'Shea V 2007 Characterization studies of two novel active pixel sensors Opt. Eng. 46 124003 Bohndiek S E et al 2008 Comparison of methods for estimating the conversion gain of CMOS active pixel sensors IEEE Sensors 10 1734–44 Charles P H, Cranmer-Sargison G, Thwaites D I, Crowe S B, Kairn T, Knight R T, Kenny J, Langton C M and Trapp J V 2014 A practical and theoretical definition of very small field size for radiotherapy output factor measurements Med. Phys. 41 041707 4397
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