Proposed fast performance evaluation of an imaging system with a discrete detector array Yi-Chin Fang,1 Ho-Lin Tsay,2,* and Guo-Yi Huang1 1
National Kaohsiung First University of Science and Technology, No. 1, University Rd., Yanchao Dist., Kaohsiung City 824, Taiwan 2
Instrument Technology Research Center, National Applied Research Laboratories, No. 20, R&D Road VI., Science Park, Hsinchu City 300, Taiwan *Corresponding author: [email protected] Received 2 May 2014; revised 11 July 2014; accepted 24 July 2014; posted 24 July 2014 (Doc. ID 211302); published 18 September 2014
This paper proposes a newly developed fast measurement of a modulation transfer function (MTF) optical system inclusive of on-axis and off-axis measurement. First, we discuss how a description of an imager in terms of its optical transfer function is not appropriate for a discrete imaging system when aliasing occurs, since these optical systems transform high spatial frequencies into low frequencies; we then measure how an efficient microscanning method could remove the aliasing effects from assigned telecentric optics and nontelecentric optics. A knife edge function and a slit function as a light source are employed in this measurement. The experiment with the newly designed MTF measurement system synchronizes on-axis and off-axis measurement. In addition, a microscan method with a specially written macro is introduced in this experiment to eliminate aliasing effects. After simulation and experimental analysis, first the slit function as a target delivers decent MTF repeatability for this newly developed MTF measurement system, which synchronizes with on-axis and off-axis measurement simply in 2 s after all equipment is ready and aligned. Second, after the six-step microscanning, aliasing will be eliminated to near zero in most cases. Finally, it is concluded that during the microscan, there is no difference between telecentric and nontelecentric optics. © 2014 Optical Society of America OCIS codes: (110.0110) Imaging systems; (120.0120) Instrumentation, measurement, and metrology. http://dx.doi.org/10.1364/AO.53.00H195
1. Introduction
Traditionally, the performance of optical image systems has been specified in terms of their optical transfer function (OTF) [1]. This measurement assume a linear system and is measured with respect to spatial frequencies in the scene [2]. However, digitalized image systems commonly seen on the market, such as CCD and complementary metaloxide semiconductor cameras, reflected a lack of anisoplanatism observed with the detector arrays when measured using the more usual definition of the
1559-128X/14/29H195-07$15.00/0 © 2014 Optical Society of America
modulation transfer function (MTF). This usual definition is perfectly adequate for continuously sampled systems but produces variable results when applied to discretely sampled systems; the results depend on the position of the sine wave in the scene [3,4]. Therefore, the discrete modulation transfer function (DMTF) was defined for an optical imager with discrete detector arrays. On the basis of the DMTF, it is first proposed that two measurement methods are introduced: the knife edge function and slit function. The application of a microscanning method is expected to eliminate the aliasing effect in this experiment. The aliasing effect plays a role in image quality of the digitalized imager in terms of insufficient sampling; therefore, these 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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optical systems transform high spatial frequencies into low frequencies from the point view of the MTF curve. The microscanning method has been employed [5–9] for various purposes. A newly developed MTF measurement system is demonstrated in this experiment in order to not only achieve fast measurement but also synchronize with on-axis and off-axis measurement. This MTF measurement system is expected to complete the measurement procedure in up to 2 s. Several telecentric lenses and nontelecentric lenses are assigned to be tested, because we want to discover if there is any measurement deviation with microscanning between telecentric optics and nontelecentric optics. Section 2 will explain what DMTF is. Section 3 will demonstrate the methodology and setup of the experiments for fast MTF measurement. Section 4 will show the measurement results and analysis. Section 5 will be the conclusion. 2. Modulation Transfer Function for an Optical System with a Discrete Detector Array A.
Introduction to the DMTF
Traditionally, the OTF and its module, MTF, are employed as standard tools of evaluation of the performance of an optical system. Both of these measures assume a linear system and are measured with respect to the spatial frequencies in the scene. If the scene is represented as an array of intensities f m, then an image of this scene gi produced by an imaging system is given by [2–4] gi
X
f mhi − m;
(1)
m
where h is the impulse response function, otherwise known as the point spread function (PSF) of the system. Written in this form it assumes that the imaging system is shift invariant. This simplifies the mathematics and is a valid approximation over some limited region of the image, even if this region is minutely small. The convolution represented by Eq. (1) may be expressed as a product in Fourier space, i.e., Gu Fu · Hu:
B. Introduction to the Aliasing Effect
This occurs when the Nyquist frequency, which is half the sampling frequency, is less than the highest spatial frequency u for which Hu is nonzero. With regard to performance measures for imaging systems with discrete detector arrays, the effect of aliasing is to remap spatial frequencies k in the scene above the Nyquist frequency onto spatial frequencies (k-IN) below the Nyquist frequency. Here N is the sampling frequency and I is an integer. The aliased high frequencies combine with the genuine lower spatial frequencies and corrupt the image. The use of microscanning [10] can increase the sampling rate and overcome the problem of aliasing, but this is not used universally in optical systems employing FPA detectors. Aliasing can also be removed using antialiasing filters, which eliminate spatial frequencies above the Nyquist frequency. This produces a cosmetically better-looking image but also removes
(2)
The quantity H as the discrete Fourier transform of the PSF is complex. It is the discrete OTF, and its modulus is the DMTF. The DMTF usually has a value of unity at low spatial frequencies and falls with increasing spatial frequency due to aberrations in the system. The optics of an imaging system is linear, and for this H has a high frequency cutoff due to the diffraction limit. The other components of an imaging system such as the detector, electronics, and display have their own transfer functions, and the overall OTF is the product of the individual OTFs. These other components can attenuate high spatial frequencies still further and can introduce noise, H196
which in effect lowers the high spatial frequency cutoff of the system. Analogue systems below saturation are generally linear, and for these a measurement of MTF is valid. But for digital or discretely sampled systems, as represented by Eq. (1), spatial frequencies above the Nyquist frequency are remapped onto lower frequencies and the usual MTF is no longer valid. This is a particular problem for imaging systems employing focal plane arrays (FPAs) of detector elements. The introduction of the DMTF removed the lack of anisoplanatism observed with the detector arrays when measured using the more usual definition of the MTF, which is the contrast in the image of a sine wave in the scene. This usual definition is perfectly adequate for continuously sampled systems but produces variable results when applied to discretely sampled systems; the result depends on the position of the sine wave in the scene. Maximum and minimum values of an MTF measured in this way are illustrated in Fig. 1.
APPLIED OPTICS / Vol. 53, No. 29 / 10 October 2014
Fig. 1. Dotted lines show the maximum and minimum values of the MTF. The solid line shows the DMTF [2].
information and makes objects in the scene more difficult to recognize [11]. 3. Methodology and Setup of Experiments A.
Introduction to the Microscanning Method
Microscanning is a technique that allows us to double the resolution of a given staring array imager. It consists in taking multiple images of the same scene, each time displacing the image over the detector plane by a distance equal to a fraction of the detector pitch. The technique is limited by the time required to shift the image from one point to the other and by the precision of the movements [12]. With the sampling of identical pixels in several frames of the specimen by moving the sensor with a piezo mechanism in a regular raster, those subimages are combined into a sharp resulting image. For example, three positions on the x and y axes increase the image size by a factor of 9, such as from the common 1388 × 1040 pixels to 4164 × 3120 pixels. Figures 2 and 3 demonstrate the star pattern with and without microscanning. In this paper, a microscanning method is employed to eliminate the aliasing effects in order to accurately
measure the MTF. In addition, we measured how efficiently the microscanning method could remove the aliasing effects from telecentric optics and nontelecentric optics when observing on-axis and off-axis scanning of the optical image. B. Methodology
This research proposes a newly developed MTF system that synchronizes with on-axis and off-axis measurement and a microscanning method. In order to achieve quick and accurate on-axis and off-axis MTF measurement at the same time, we employed an integrating sphere light source; light is supposed to directly pass through detected optics, with auxiliary light reflecting from mirrors with multiple coatings. Both images from on-axis and off-axis will appear at the sensor simultaneously, because a special optical system layout with an additional mirror was included. With regard to the issue of alignment, we precisely align the optics axis and image sensor with the assistance of a micro-triaxial rotating machine. When microscanning is in process, the image sensor will be well aligned on the three-axis platform with micromobile imaging sensor scans in order to achieve best results; the MTF of the detected optics will be precisely calculated by an algorithm written by the lab. C. Setup of a Newly Developed MTF Measurement System that Synchronizes with On-Axis and Off-Axis Measurement and a Microscanning Method
1. Demonstration of Optical System Layout in This Experiment Figure 4 shows the optical system layout of this experiment inclusive of a light source, eight reflecting mirrors, and a CCD. Figure 5 is a picture of the real optical system layout inclusive of a light source, eight reflecting mirrors, a triaxial platform, and a CCD. Fig. 2. Star pattern.
Fig. 4. Optical system layout of this experiment inclusive of light source, eight reflecting mirrors, and CCD.
Fig. 3. Star pattern after four-step microscanning.
Fig. 5. Picture of the real optical system layout inclusive of light source, eight reflecting mirrors, triaxial platform, and CCD. 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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2.
Summary of Experimental Equipment
Equipment for Experiments Light source
Reflector
Micro-triaxial translation stages Sensor
Labsphere integrating sphere; diameter is 20 cm and exitance is 5 cm in diameter. Light source is set as its color temperature at 3000 K (without filter). Both images from on-axis and off axis will appear at sensor simultaneously because of special optical system layout with additional mirror included. SIGMA KOKI CO., LTD (one step is 50 nm) (CCD) Basler A311f mono image sensor, linear response
3. Summary of Optics and Specifications in This Experiment Lens Specification
Telecentric lens
Nontelecentric lens
Contax 21 mm Contax 28 mm Chilin 576 Voigtlander 15 mm Voigtlander 25 mm Chilin 720
Focal Lengths (mm)
Picture Angle
FNumber
21
92°
2.8–22
28
74°
2–22
19.2–24.1 15
110°
2.4–2.52 4.5–22
25
82°
4–22
24.0–30.1
2.4–2.55
Fig. 6. Images of the slit for on-axis and off-axis at sensor.
B. Knife Edge Employed in This Experiment
Knife edge is an alternative light source as the target of the MTF measurement. It takes great advantage of the fact that microscanning will be no longer required if the knife edge is rotated at 4.76°. The reason given is that the rotated knife edge might get sufficient sampling in this experiment. Compared to the slit light source, measure by the knife edge might save much more time. Figures 7 and 8 show knife edge and slit images, respectively, for on-axis and offaxis on the sensor (vertical and horizontal). Table 1 is the comparison of measurement times for the slit and knife edge functions in this experiment. C.
In this experiment, we analyze the result of microscanning of the slit function versus different numbers of steps. Figure 9 shows the telecentric Contax 21 mm F2.8 RTS lens with differing number of step microscanning. We did more steps, and we derived a better and smoother MTF, especially in high spatial frequencies. For most cases, we could conclude that the MTF curve becomes smoother in high frequencies after six-step microscanning. D.
4. Experimental Steps Step 1: System setup and alignment Step 2: Slit and knife edge are employed in this experiment. Step 3: Newly developed MTF system that synchronizes with on-axis and off-axis measurement Step 4: Microscanning: 1 step, 2 steps, 3 steps, 4 steps, 6 steps, and 12 steps Step 5: Telecentric and nontelecentric lenses are employed.
Slit as a Light Source and Microscanning Procedure
MTF Calculation Procedure
Figures 10–14 demonstrate the MTF calculation process for the slit and edge images. The image of the slit was extracted to get the line spread function and processed to get the MTF curve by a fast Fourier
4. Analysis of Experimental Results A.
Slit Employed in This Experiment
Imaging through on-axis and off-axis will work on the sensor at the same time thanks to this newly developed MTF measurement system. The employment of an additional mirror will make measurement very fast for either on-axis or off-axis. However, magnification of the slit on the mirror might be more or less than 1.0 so that deviation of the magnification of the slit, which might introduce errors, will be compensated by an algorithm written for this experiment. The slit as the light source will be employed horizontally and vertically as in Fig. 6. H198
APPLIED OPTICS / Vol. 53, No. 29 / 10 October 2014
Fig. 7. Pictures of the rotated knife edge images for on-axis and off-axis on the sensor.
Table 1.
Comparison of Knife Edge and Slit Measurement Times in This Experiment
Procedure Microscanning Knife edge
focus → confirm →microscanning (10 steps) focus → confirm
Measurement Time (s) 60 3
transform. The edge image was processed with the same procedure to get the MTF curve, with one more differentiation step to get the line spread function from the edge spread function.
Fig. 11. MTF calculation process for edge image. Upper and upper-right is the image of measuring area for horizontal and vertical directions. Bottom-left is derived line spread function, and bottom-right is the derived MTF curve.
Fig. 8. Four slit images are on the sensor for microscanning.
Fig. 12. MTF measure result by slit as light source on axis. Upper is the image of measuring area. Bottom-right is line spread function, and bottom-left is the derived MTF curve.
Fig. 9. Curves for telecentric Contax 21 mm F2.8 RTS lens with different numbers of steps for microscanning.
Fig. 13. MTF measure by slit as light source off-axis. Upper is the image of measuring area. Bottom-right is line spread function, and bottom-left is the derived MTF curve.
E. Analysis of Microscanning for the MTF Measurement by the Slit Source
Fig. 10. MTF calculation process for slit image. Upper is the image of measuring area. Bottom-right is line spread function, and bottom-left is the derived MTF curve.
Figure 15 demonstrates the through focus MTF curves. In Fig. 15, the blue ray is saggital and the red is tangential. 80, 100 and 120 line pairs (lp/mm) are represented in these experiments and indicated by arrows in different colors. Figure 16 shows an on-axis and three off-axis MTF curves. The white line is on-axis saggital and The 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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Fig. 14. MTF measurement by knife edge on axis. MTF curve, line spread function and captured image are shown in right, left, and inlet of right, respectively. Fig. 18. Deviation of MTF measurement due to different numbers of microscanning steps off-axis.
Fig. 15. Through focus curves for four measuring points in the spatial frequencies 80, 100, and 120 lp∕mm.
Fig. 19. Results of MTF measurement of Contax 21 mm lens with microscanning (1 step, 2 steps, 3 steps, 4 steps, 6 steps, and 12 steps).
dots are on-axis tangential. The red and blue lines are similar. From Figs. 17 and 18, it is assumed that MTF measurement with six-step microscanning will remove most aliasing effects in this experiment, as shown in Figs. 19 and 20.
1.0
Fig. 16. MTF curves for an on-axis and 3 off-axis points.
1 Step Micro Scanning. 2 Step Micro Scanning. 5 Step Micro Scanning. 10(ALL) Step Micro Scanning.
Modulation Transfer Function.
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0
10
20
30
40
50
60
70
80
90 100 110 120 130 140 150
Spatial Frequency.(lp/mm)
Fig. 17. Deviation of MTF measurement due to different numbers of microscanning steps on-axis. H200
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Fig. 20. Measured results of many different lenses with various numbers of microscanning steps (1 step, 2 steps, 5 steps, and 10 steps).
5. Conclusion
1. We reach success with this newly designed MTF measurement system, which synchronizes with on-axis and off-axis measurement. 2. After simulation and experimental analysis, the slit function as a target delivers decent MTF repeatability for this newly developed MTF measurement system, which synchronize with on-axis and off-axis measurement simply in 2 s after all equipment is ready and aligned, although it takes longer for the microscanning procedure. 3. The aliasing effect will be reduced to a minimum after six-step microscanning in this experiment. 4. During the microscanning process, we were not able to find a difference between telecentric optics and nontelecentric optics from the experiments. References 1. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. A 231, 91–103 (1955). 2. A. H. Lettington, D. Dunn, A. M. Fairhurst, and Y. Fang, “Proposed performance measures for imaging systems with discrete detector arrays,” J. Mod. Opt. 48, 115–123 (2001).
3. A. H. Lettington and Q. H. Hong, “A discrete modulation transfer function for focal plane arrays,” Infrared Phys. 34, 109–114 (1993). 4. A. H. Lettington and Q. H. Hong, “Measurement of the discrete modulation transfer function,” J. Mod. Opt. 40, 203–212 (1993). 5. J. Shi, S. E. Reichenbach, and J. D. Howe, “Small-kernel superresolution methods for microscanning imaging systems,” Appl. Opt. 45, 1203–1214 (2006). 6. O. Nakamura and M. Goto, “Four-beam laser interferometry for three-dimensional microscopic coordinate measurement,” Appl. Opt. 33, 31–36 (1994). 7. J.-H. Park, K. Hong, and B. Lee, “Recent progress in threedimensional information processing based on integral imaging,” Appl. Opt. 48, H77–H94 (2009). 8. X. Wang and Q. Guo, “Enhancing computational integral imaging performance using an interpolation method based on non-zero-pixel derivation,” Appl. Opt. 49, 3997–4003 (2010). 9. X. Wang, J. Zhang, Z. Feng, and H. Chang, “Relationship between microscanned image quality and fill factor of detectors,” Appl. Opt. 44, 4470–4474 (2005). 10. D. J. Bradley, C. J. Baddiley, and P. N. J. Dennis, “The modulation transfer function of focal plane array systems,” Proc. SPIE 0807, 33–41 (1987). 11. A. M. Fairhurst and A. H. Lettington, “Method of predicting the probability of human observer recognition targets in simulated thermal images,” Opt. Eng. 37, 744–751 (1998). 12. J. Fortin and P. C. Chevrette, “Realization of a fast microscanning device for infrared focal plane arrays,” Proc. SPIE 2743, 185–196 (1996).
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National Kaohsiung First University of Science and Technology, No. 1, University Rd., Yanchao Dist., Kaohsiung City 824, Taiwan 2
Instrument Technology Research Center, National Applied Research Laboratories, No. 20, R&D Road VI., Science Park, Hsinchu City 300, Taiwan *Corresponding author: [email protected] Received 2 May 2014; revised 11 July 2014; accepted 24 July 2014; posted 24 July 2014 (Doc. ID 211302); published 18 September 2014
This paper proposes a newly developed fast measurement of a modulation transfer function (MTF) optical system inclusive of on-axis and off-axis measurement. First, we discuss how a description of an imager in terms of its optical transfer function is not appropriate for a discrete imaging system when aliasing occurs, since these optical systems transform high spatial frequencies into low frequencies; we then measure how an efficient microscanning method could remove the aliasing effects from assigned telecentric optics and nontelecentric optics. A knife edge function and a slit function as a light source are employed in this measurement. The experiment with the newly designed MTF measurement system synchronizes on-axis and off-axis measurement. In addition, a microscan method with a specially written macro is introduced in this experiment to eliminate aliasing effects. After simulation and experimental analysis, first the slit function as a target delivers decent MTF repeatability for this newly developed MTF measurement system, which synchronizes with on-axis and off-axis measurement simply in 2 s after all equipment is ready and aligned. Second, after the six-step microscanning, aliasing will be eliminated to near zero in most cases. Finally, it is concluded that during the microscan, there is no difference between telecentric and nontelecentric optics. © 2014 Optical Society of America OCIS codes: (110.0110) Imaging systems; (120.0120) Instrumentation, measurement, and metrology. http://dx.doi.org/10.1364/AO.53.00H195
1. Introduction
Traditionally, the performance of optical image systems has been specified in terms of their optical transfer function (OTF) [1]. This measurement assume a linear system and is measured with respect to spatial frequencies in the scene [2]. However, digitalized image systems commonly seen on the market, such as CCD and complementary metaloxide semiconductor cameras, reflected a lack of anisoplanatism observed with the detector arrays when measured using the more usual definition of the
1559-128X/14/29H195-07$15.00/0 © 2014 Optical Society of America
modulation transfer function (MTF). This usual definition is perfectly adequate for continuously sampled systems but produces variable results when applied to discretely sampled systems; the results depend on the position of the sine wave in the scene [3,4]. Therefore, the discrete modulation transfer function (DMTF) was defined for an optical imager with discrete detector arrays. On the basis of the DMTF, it is first proposed that two measurement methods are introduced: the knife edge function and slit function. The application of a microscanning method is expected to eliminate the aliasing effect in this experiment. The aliasing effect plays a role in image quality of the digitalized imager in terms of insufficient sampling; therefore, these 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
H195
optical systems transform high spatial frequencies into low frequencies from the point view of the MTF curve. The microscanning method has been employed [5–9] for various purposes. A newly developed MTF measurement system is demonstrated in this experiment in order to not only achieve fast measurement but also synchronize with on-axis and off-axis measurement. This MTF measurement system is expected to complete the measurement procedure in up to 2 s. Several telecentric lenses and nontelecentric lenses are assigned to be tested, because we want to discover if there is any measurement deviation with microscanning between telecentric optics and nontelecentric optics. Section 2 will explain what DMTF is. Section 3 will demonstrate the methodology and setup of the experiments for fast MTF measurement. Section 4 will show the measurement results and analysis. Section 5 will be the conclusion. 2. Modulation Transfer Function for an Optical System with a Discrete Detector Array A.
Introduction to the DMTF
Traditionally, the OTF and its module, MTF, are employed as standard tools of evaluation of the performance of an optical system. Both of these measures assume a linear system and are measured with respect to the spatial frequencies in the scene. If the scene is represented as an array of intensities f m, then an image of this scene gi produced by an imaging system is given by [2–4] gi
X
f mhi − m;
(1)
m
where h is the impulse response function, otherwise known as the point spread function (PSF) of the system. Written in this form it assumes that the imaging system is shift invariant. This simplifies the mathematics and is a valid approximation over some limited region of the image, even if this region is minutely small. The convolution represented by Eq. (1) may be expressed as a product in Fourier space, i.e., Gu Fu · Hu:
B. Introduction to the Aliasing Effect
This occurs when the Nyquist frequency, which is half the sampling frequency, is less than the highest spatial frequency u for which Hu is nonzero. With regard to performance measures for imaging systems with discrete detector arrays, the effect of aliasing is to remap spatial frequencies k in the scene above the Nyquist frequency onto spatial frequencies (k-IN) below the Nyquist frequency. Here N is the sampling frequency and I is an integer. The aliased high frequencies combine with the genuine lower spatial frequencies and corrupt the image. The use of microscanning [10] can increase the sampling rate and overcome the problem of aliasing, but this is not used universally in optical systems employing FPA detectors. Aliasing can also be removed using antialiasing filters, which eliminate spatial frequencies above the Nyquist frequency. This produces a cosmetically better-looking image but also removes
(2)
The quantity H as the discrete Fourier transform of the PSF is complex. It is the discrete OTF, and its modulus is the DMTF. The DMTF usually has a value of unity at low spatial frequencies and falls with increasing spatial frequency due to aberrations in the system. The optics of an imaging system is linear, and for this H has a high frequency cutoff due to the diffraction limit. The other components of an imaging system such as the detector, electronics, and display have their own transfer functions, and the overall OTF is the product of the individual OTFs. These other components can attenuate high spatial frequencies still further and can introduce noise, H196
which in effect lowers the high spatial frequency cutoff of the system. Analogue systems below saturation are generally linear, and for these a measurement of MTF is valid. But for digital or discretely sampled systems, as represented by Eq. (1), spatial frequencies above the Nyquist frequency are remapped onto lower frequencies and the usual MTF is no longer valid. This is a particular problem for imaging systems employing focal plane arrays (FPAs) of detector elements. The introduction of the DMTF removed the lack of anisoplanatism observed with the detector arrays when measured using the more usual definition of the MTF, which is the contrast in the image of a sine wave in the scene. This usual definition is perfectly adequate for continuously sampled systems but produces variable results when applied to discretely sampled systems; the result depends on the position of the sine wave in the scene. Maximum and minimum values of an MTF measured in this way are illustrated in Fig. 1.
APPLIED OPTICS / Vol. 53, No. 29 / 10 October 2014
Fig. 1. Dotted lines show the maximum and minimum values of the MTF. The solid line shows the DMTF [2].
information and makes objects in the scene more difficult to recognize [11]. 3. Methodology and Setup of Experiments A.
Introduction to the Microscanning Method
Microscanning is a technique that allows us to double the resolution of a given staring array imager. It consists in taking multiple images of the same scene, each time displacing the image over the detector plane by a distance equal to a fraction of the detector pitch. The technique is limited by the time required to shift the image from one point to the other and by the precision of the movements [12]. With the sampling of identical pixels in several frames of the specimen by moving the sensor with a piezo mechanism in a regular raster, those subimages are combined into a sharp resulting image. For example, three positions on the x and y axes increase the image size by a factor of 9, such as from the common 1388 × 1040 pixels to 4164 × 3120 pixels. Figures 2 and 3 demonstrate the star pattern with and without microscanning. In this paper, a microscanning method is employed to eliminate the aliasing effects in order to accurately
measure the MTF. In addition, we measured how efficiently the microscanning method could remove the aliasing effects from telecentric optics and nontelecentric optics when observing on-axis and off-axis scanning of the optical image. B. Methodology
This research proposes a newly developed MTF system that synchronizes with on-axis and off-axis measurement and a microscanning method. In order to achieve quick and accurate on-axis and off-axis MTF measurement at the same time, we employed an integrating sphere light source; light is supposed to directly pass through detected optics, with auxiliary light reflecting from mirrors with multiple coatings. Both images from on-axis and off-axis will appear at the sensor simultaneously, because a special optical system layout with an additional mirror was included. With regard to the issue of alignment, we precisely align the optics axis and image sensor with the assistance of a micro-triaxial rotating machine. When microscanning is in process, the image sensor will be well aligned on the three-axis platform with micromobile imaging sensor scans in order to achieve best results; the MTF of the detected optics will be precisely calculated by an algorithm written by the lab. C. Setup of a Newly Developed MTF Measurement System that Synchronizes with On-Axis and Off-Axis Measurement and a Microscanning Method
1. Demonstration of Optical System Layout in This Experiment Figure 4 shows the optical system layout of this experiment inclusive of a light source, eight reflecting mirrors, and a CCD. Figure 5 is a picture of the real optical system layout inclusive of a light source, eight reflecting mirrors, a triaxial platform, and a CCD. Fig. 2. Star pattern.
Fig. 4. Optical system layout of this experiment inclusive of light source, eight reflecting mirrors, and CCD.
Fig. 3. Star pattern after four-step microscanning.
Fig. 5. Picture of the real optical system layout inclusive of light source, eight reflecting mirrors, triaxial platform, and CCD. 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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2.
Summary of Experimental Equipment
Equipment for Experiments Light source
Reflector
Micro-triaxial translation stages Sensor
Labsphere integrating sphere; diameter is 20 cm and exitance is 5 cm in diameter. Light source is set as its color temperature at 3000 K (without filter). Both images from on-axis and off axis will appear at sensor simultaneously because of special optical system layout with additional mirror included. SIGMA KOKI CO., LTD (one step is 50 nm) (CCD) Basler A311f mono image sensor, linear response
3. Summary of Optics and Specifications in This Experiment Lens Specification
Telecentric lens
Nontelecentric lens
Contax 21 mm Contax 28 mm Chilin 576 Voigtlander 15 mm Voigtlander 25 mm Chilin 720
Focal Lengths (mm)
Picture Angle
FNumber
21
92°
2.8–22
28
74°
2–22
19.2–24.1 15
110°
2.4–2.52 4.5–22
25
82°
4–22
24.0–30.1
2.4–2.55
Fig. 6. Images of the slit for on-axis and off-axis at sensor.
B. Knife Edge Employed in This Experiment
Knife edge is an alternative light source as the target of the MTF measurement. It takes great advantage of the fact that microscanning will be no longer required if the knife edge is rotated at 4.76°. The reason given is that the rotated knife edge might get sufficient sampling in this experiment. Compared to the slit light source, measure by the knife edge might save much more time. Figures 7 and 8 show knife edge and slit images, respectively, for on-axis and offaxis on the sensor (vertical and horizontal). Table 1 is the comparison of measurement times for the slit and knife edge functions in this experiment. C.
In this experiment, we analyze the result of microscanning of the slit function versus different numbers of steps. Figure 9 shows the telecentric Contax 21 mm F2.8 RTS lens with differing number of step microscanning. We did more steps, and we derived a better and smoother MTF, especially in high spatial frequencies. For most cases, we could conclude that the MTF curve becomes smoother in high frequencies after six-step microscanning. D.
4. Experimental Steps Step 1: System setup and alignment Step 2: Slit and knife edge are employed in this experiment. Step 3: Newly developed MTF system that synchronizes with on-axis and off-axis measurement Step 4: Microscanning: 1 step, 2 steps, 3 steps, 4 steps, 6 steps, and 12 steps Step 5: Telecentric and nontelecentric lenses are employed.
Slit as a Light Source and Microscanning Procedure
MTF Calculation Procedure
Figures 10–14 demonstrate the MTF calculation process for the slit and edge images. The image of the slit was extracted to get the line spread function and processed to get the MTF curve by a fast Fourier
4. Analysis of Experimental Results A.
Slit Employed in This Experiment
Imaging through on-axis and off-axis will work on the sensor at the same time thanks to this newly developed MTF measurement system. The employment of an additional mirror will make measurement very fast for either on-axis or off-axis. However, magnification of the slit on the mirror might be more or less than 1.0 so that deviation of the magnification of the slit, which might introduce errors, will be compensated by an algorithm written for this experiment. The slit as the light source will be employed horizontally and vertically as in Fig. 6. H198
APPLIED OPTICS / Vol. 53, No. 29 / 10 October 2014
Fig. 7. Pictures of the rotated knife edge images for on-axis and off-axis on the sensor.
Table 1.
Comparison of Knife Edge and Slit Measurement Times in This Experiment
Procedure Microscanning Knife edge
focus → confirm →microscanning (10 steps) focus → confirm
Measurement Time (s) 60 3
transform. The edge image was processed with the same procedure to get the MTF curve, with one more differentiation step to get the line spread function from the edge spread function.
Fig. 11. MTF calculation process for edge image. Upper and upper-right is the image of measuring area for horizontal and vertical directions. Bottom-left is derived line spread function, and bottom-right is the derived MTF curve.
Fig. 8. Four slit images are on the sensor for microscanning.
Fig. 12. MTF measure result by slit as light source on axis. Upper is the image of measuring area. Bottom-right is line spread function, and bottom-left is the derived MTF curve.
Fig. 9. Curves for telecentric Contax 21 mm F2.8 RTS lens with different numbers of steps for microscanning.
Fig. 13. MTF measure by slit as light source off-axis. Upper is the image of measuring area. Bottom-right is line spread function, and bottom-left is the derived MTF curve.
E. Analysis of Microscanning for the MTF Measurement by the Slit Source
Fig. 10. MTF calculation process for slit image. Upper is the image of measuring area. Bottom-right is line spread function, and bottom-left is the derived MTF curve.
Figure 15 demonstrates the through focus MTF curves. In Fig. 15, the blue ray is saggital and the red is tangential. 80, 100 and 120 line pairs (lp/mm) are represented in these experiments and indicated by arrows in different colors. Figure 16 shows an on-axis and three off-axis MTF curves. The white line is on-axis saggital and The 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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Fig. 14. MTF measurement by knife edge on axis. MTF curve, line spread function and captured image are shown in right, left, and inlet of right, respectively. Fig. 18. Deviation of MTF measurement due to different numbers of microscanning steps off-axis.
Fig. 15. Through focus curves for four measuring points in the spatial frequencies 80, 100, and 120 lp∕mm.
Fig. 19. Results of MTF measurement of Contax 21 mm lens with microscanning (1 step, 2 steps, 3 steps, 4 steps, 6 steps, and 12 steps).
dots are on-axis tangential. The red and blue lines are similar. From Figs. 17 and 18, it is assumed that MTF measurement with six-step microscanning will remove most aliasing effects in this experiment, as shown in Figs. 19 and 20.
1.0
Fig. 16. MTF curves for an on-axis and 3 off-axis points.
1 Step Micro Scanning. 2 Step Micro Scanning. 5 Step Micro Scanning. 10(ALL) Step Micro Scanning.
Modulation Transfer Function.
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0
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Spatial Frequency.(lp/mm)
Fig. 17. Deviation of MTF measurement due to different numbers of microscanning steps on-axis. H200
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Fig. 20. Measured results of many different lenses with various numbers of microscanning steps (1 step, 2 steps, 5 steps, and 10 steps).
5. Conclusion
1. We reach success with this newly designed MTF measurement system, which synchronizes with on-axis and off-axis measurement. 2. After simulation and experimental analysis, the slit function as a target delivers decent MTF repeatability for this newly developed MTF measurement system, which synchronize with on-axis and off-axis measurement simply in 2 s after all equipment is ready and aligned, although it takes longer for the microscanning procedure. 3. The aliasing effect will be reduced to a minimum after six-step microscanning in this experiment. 4. During the microscanning process, we were not able to find a difference between telecentric optics and nontelecentric optics from the experiments. References 1. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. A 231, 91–103 (1955). 2. A. H. Lettington, D. Dunn, A. M. Fairhurst, and Y. Fang, “Proposed performance measures for imaging systems with discrete detector arrays,” J. Mod. Opt. 48, 115–123 (2001).
3. A. H. Lettington and Q. H. Hong, “A discrete modulation transfer function for focal plane arrays,” Infrared Phys. 34, 109–114 (1993). 4. A. H. Lettington and Q. H. Hong, “Measurement of the discrete modulation transfer function,” J. Mod. Opt. 40, 203–212 (1993). 5. J. Shi, S. E. Reichenbach, and J. D. Howe, “Small-kernel superresolution methods for microscanning imaging systems,” Appl. Opt. 45, 1203–1214 (2006). 6. O. Nakamura and M. Goto, “Four-beam laser interferometry for three-dimensional microscopic coordinate measurement,” Appl. Opt. 33, 31–36 (1994). 7. J.-H. Park, K. Hong, and B. Lee, “Recent progress in threedimensional information processing based on integral imaging,” Appl. Opt. 48, H77–H94 (2009). 8. X. Wang and Q. Guo, “Enhancing computational integral imaging performance using an interpolation method based on non-zero-pixel derivation,” Appl. Opt. 49, 3997–4003 (2010). 9. X. Wang, J. Zhang, Z. Feng, and H. Chang, “Relationship between microscanned image quality and fill factor of detectors,” Appl. Opt. 44, 4470–4474 (2005). 10. D. J. Bradley, C. J. Baddiley, and P. N. J. Dennis, “The modulation transfer function of focal plane array systems,” Proc. SPIE 0807, 33–41 (1987). 11. A. M. Fairhurst and A. H. Lettington, “Method of predicting the probability of human observer recognition targets in simulated thermal images,” Opt. Eng. 37, 744–751 (1998). 12. J. Fortin and P. C. Chevrette, “Realization of a fast microscanning device for infrared focal plane arrays,” Proc. SPIE 2743, 185–196 (1996).
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