Off-axis digital holographic microscopy with LED illumination based on polarization filtering Rongli Guo,1,2 Baoli Yao,1,* Peng Gao,1 Junwei Min,1 Meiling Zhou,1 Jun Han,2 Xun Yu,2 Xianghua Yu,1 Ming Lei,1 Shaohui Yan,1 Yanlong Yang,1 Dan Dan,1 and Tong Ye1 1
State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China 2
Xi’an Technological University, Xi’an 710032, China *Corresponding author: [email protected]
Received 30 September 2013; revised 28 October 2013; accepted 28 October 2013; posted 29 October 2013 (Doc. ID 198529); published 25 November 2013
A reflection mode digital holographic microscope with light emitting diode (LED) illumination and offaxis interferometry is proposed. The setup is comprised of a Linnik interferometer and a grating-based 4f imaging unit. Both object and reference waves travel coaxially and are split into multiple diffraction orders in the Fourier plane by the grating. The zeroth and first orders are filtered by a polarizing array to select orthogonally polarized object waves and reference waves. Subsequently, the object and reference waves are combined again in the output plane of the 4f system, and then the hologram with uniform contrast over the entire field of view can be acquired with the aid of a polarizer. The one-shot nature in the off-axis configuration enables an interferometric recording time on a millisecond scale. The validity of the proposed setup is illustrated by imaging nanostructured substrates, and the experimental results demonstrate that the phase noise is reduced drastically by an order of 68% when compared to a He–Ne laser-based result. © 2013 Optical Society of America OCIS codes: (090.2880) Holographic interferometry; (180.3170) Interference microscopy; (120.3180) Interferometry; (120.5050) Phase measurement. http://dx.doi.org/10.1364/AO.52.008233
1. Introduction
Digital holographic microscopy (DHM) is a promising 3D imaging technology that allows the investigation of the shape of engineered surfaces or tomography of biological samples with microscale lateral resolution and nanoscale axial precision [1]. Over the past decades, thanks to newly available CCD cameras, high performance of computers, and advances in offline numerical processing techniques, DHM has been fully developed and successfully applied in diverse applications; for instance, in quantitative biology microscopy [2–7], surface relief characterization of 1559-128X/13/348233-06$15.00/0 © 2013 Optical Society of America
MEMS or other microstructures [8–12], topography of micro-optics [13–16], and so on [17–20]. Usually, coherent light sources, i.e., lasers, are adopted in DHM as illumination light, and the quality of holograms is inevitably degraded by the inherent coherent noise. When the complex object wave is numerically reconstructed from a hologram, not only is a useful phase image embedded but also phase noise (phase error) is introduced by such noises. The higher the phase noise is, the lower the measurement precision. To overcome the coherent noise, coherent lasers are replaced by light sources of partial coherence (partial temporal coherent light or partial spatial coherent light) [21–37]. Nevertheless, a light emitting diode (LED) as a light source for DHMs has not yet been fully exploited [30–37]. The principle in 1 December 2013 / Vol. 52, No. 34 / APPLIED OPTICS
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LED light source (as well as with other short time coherence light source) illuminated DHM is optical path length compensation between an object and reference arms, which is achieved by using optics pairs in both arms, as in a Michelson or a Mach– Zehnder interferometer [32–37]. However, the limited coherent length of such light sources, typically on the order of a few micrometers, hinders its application in an off-axis DHM, since just a limited number of interference fringes appear in the FOV. For this reason, temporal phase-shifting interferometry (TPSI) is more preferable, as demonstrated in most of the previous works [32–36]. Though TPSI can eliminate the direct component (DC) term and the unwanted twin image in the numerical reconstruction process, it renders some specific disadvantages when compared to the off-axis interferometry: the time resolution is low due to the need of multiple phase shifting operation; it suffers from a phase shifting error introduced by the miscalibration of the piezoelectric transducer or other phase shifting parts; and it is sensitive to the vibration caused by environmental disturbance. Recently, Dubois and Yourassowsky [37] have proposed an off-axis scheme with an LED light source, based on a Mach–Zehnder interferometer, in which a transmission grating was used to ensure an optical path difference (OPD) match between an object wave and a reference wave so that high fringe contrast was obtained in the whole FOV of the hologram. It has the advantage of one-shot full-field acquisition. However, up to three lenses were used in the reference arm for OPD compensation. It brings difficulty in the precise transverse alignment between the object and reference arms as well as increased complexity of the system. Bhaduri et al. [21] have also demonstrated the application of a halogen lamp light source in a grating-based diffraction phase interferometer. The zeroth order wave of the grating was low-pass filtered by a pin hole to generate a reference wave, whereas the first order wave passed through being untouched to act as object wave. The main limitation of this configuration is that the pinhole filtering leads to a large portion of energy loss in zeroth order beam and puts high demand on collimation of the illumination wave, which is relative a hard task for cheap LED beads. In this paper, we present an off-axis DHM with LED illumination by the use of a cheap LED bead in reflection mode, and demonstrate its application in the measurement of engineered nanostructured surfaces. The apparatus consists of two parts: a standard Linnik-type interferometer and a 4f spatial polarization filtering system. A grating is placed in conjugation with the CCD plane to provide dense interference fringes over the whole field of view. This configuration partially overcomes drawbacks presented in [21,37], i.e., only one additional objective is used for OPD match and has less energy loss, as there is no pinhole filtering, which brings convenience in optics elements alignment. The advantage 8234
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stemming from an LED light source is its low phase noise imaging capability. 2. Principal of Polarization Filtering and Experiment Setup
The scheme of the proposed polarization filtering offaxis interferometry is shown in Fig. 1(a). Two lenses, L1 and L2 , are placed in a confocal way to form a 4f imaging system. Linear grating G with period d is placed in the front focal plane of lens L1 while the CCD camera is placed in the back focal plane of lens L2 to record holograms. Vertically linearly polarized object waves and horizontally linearly polarized reference waves propagate along the optical axis and incident onto the grating G. The grating splits both the object and reference waves into multiple copies along its different diffraction orders, and different copies are separated in the Fourier plane. A polarization filter is placed at the Fourier plane to implement orthogonally polarization filtering on both the zeroth and first order waves. As depicted in Fig. 1(a), the filter consists of two rectangular opening masks; in the upper mask (has a size of 3 mm × 3 mm) a polarizer is placed with the polarization orientation parallel to that of the object wave, while in the bottom mask (has a size of 3 mm × 3 mm) a polarizer is placed with its polarization orientation perpendicular to the upper one. The zeroth order wave is filtered so that only the object wave passes, whereas the first order is filtered to pass only the reference wave. The lens L2 reshapes both the object wave and reference wave again. Polarizer P is set to convert two orthogonally polarized waves into the same polarization orientation for interference in the CCD plane. The grating is placed
Fig. 1. Polarization filtering and interference imaging: (a) schematic of 4f spatial filtering and off-axis interferometry; (b) interference fringes obtained without grating and polarization filter; (c) fringes taken with proposed scheme. Only stripes (1024 × 200 pixels) of the whole holograms are shown in (b) and (c). O and R, vertically polarized object wave and horizontally polarized reference wave, respectively; G is the, grating; L1 ∼ L2 are the lenses; P is the linear polarizer; and the polarization filter placed at the Fourier plane of lens L1 is comprised of two polarizers with orthogonal polarizations.
conjugated with the CCD plane to maintain the spatial cross correlation and the OPD match between object and reference waves [21,37]. Therefore, an interferogram with uniform contrast over the whole FOV is obtained even with reduced coherence light sources in this off-axis configuration. Figure 1(b) shows a stripe of the interferogram acquired without using the grating and the polarization filter, but just tilting the mirror M 1 [see Fig. 2] in the reference wave path. It can be seen that the fringes have uneven contrast. At the two side borders of the hologram, the contrast of fringes becomes worse. When a larger cross angle is set between the two waves, the fringe disappears rapidly. Figure 1(c) shows a same stripe size of the interferogram acquired with the grating and the polarization filtering unit. It can be seen that more dense fringes are obtained and the contrast is uniform across the entire FOV. The sketch of the experimental setup is shown in Fig. 2, which includes two parts: a Linnik-type interferometer and a 4f polarization filtering image unit. A red LED with central wavelength 630 nm and bandwidth 21 nm is used as the light source. The coherence length of the light source, 2 ln 2∕πλ2 ∕Δλ, is calculated to be 8.5 μm. The light from the LED is collimated by a telescope system comprised of a 20× microscope lens, MO1 , and a lens, L1 . A polarizer, P1 , transforms the random polarization into linear polarization. The Linnik-type interferometer consists of two identical microscope objectives, MO2 and MO3 , and two identical lenses, L2 and L3 , which are placed in symmetry to ensure OPD match between two arms. Sample S and reference mirror, M 1 , are placed in the focal planes of MO2 and MO3 , respectively. The wave reflected from mirror M 1 serves as the reference wave, whereas the wave reflected from the sample is the object wave. Polarizers P2 and P3 , with horizontal and vertical polarizations are, respectively, located in the two arms to transform the polarizations of the two waves into orthogonal polarizations. The image of the sample is projected onto the grating plane via MO3
Fig. 2. Experimental setup: NPBS is the nonpolarizing beam splitter; L1 –L5 are achromatic lenses with focal lengths of f 2 f 3 f 4 100 mm, f 5 200 mm; P1 –P4 are linear polarizers; A is the aperture; MO1 is the 20× microscope objective; MO2 and MO3 are identical microscope objectives (25×, NA 0.4); M 1 is the mirror; S is the sample; and G is a grating with period of 15 μm.
and lens L3. The object and reference waves pass through the 4f filtering image system, and then an off-axis hologram is formed in the CCD plane. The relative intensity of the two waves can be adjusted by polarizers P1 and P4 . The CCD camera has 1024 × 768 pixels, 8 bit dynamic range, and pixel size of 4.65 μm × 4.65 μm. In the setup, only the microscope objective MO2 and mirror M 1 are used for OPD match, which greatly simplifies the accurate alignment process of the setup. 3. Numerical Reconstruction
Based on the proposed setup, an off-axis interferometry for DHM is performed. We denote the unfiltered object wave as Ox; y, and the unfiltered reference wave as a constant A. For brevity of expression, we omit the influence of P4 on the amplitude of both the object and reference waves in the following expression. According to the description above, the filtered object wave O0 x; y and reference wave R1 x; y, in the CCD plane can be expressed as 1 O0 x; y a0 Ox; y ; 0
(1)
1 0 R1 x; y a1 A exp i2π x : 1 Md
(2)
Here, the subscripts denote the filtered diffraction order index. a0 and a1 are diffraction coefficients of the zeroth and the first order wave of grating G, M f 5 ∕f 4 is the magnification of the 4f image system, and x and y denote coordinates in the CCD plane. Thus, the intensity distribution of the hologram is Ix; y jO0 j2 jR1 j2 R1 O0 R1 O0 :
(3)
From Eqs. (1)–(3), we know that the hologram is a spatial modulated one with carrier frequency of 1∕Md. To suppress the DC term and the unwanted twin term, a spatial filtering technique is applied [38]. A digital reference wave RD x; y is multiplied with Ix; y, then the product RD I is Fourier transformed into the spectrum domain. The RD x; y is defined as RD x; y 1∕a1 A expi2πx∕Md, in which the carrier frequency 1∕Md can be determined from the fringe frequency of the off-axis interferogram. This manipulation shifts the spectrum of the object wave, O0 R1 RD O0 , to the original area and then it can be spatially filtered out by a low-pass digital filter mask in the spectrum domain. The complex object wave in the CCD plane can be directly obtained after an inverse Fourier transformation on the filtered spectrum. The wrapped phase image can be computed from the reconstructed complex object wave, Ox; y, given as arctanfImOx; y∕ReOx; ygmod2π. After 1 December 2013 / Vol. 52, No. 34 / APPLIED OPTICS
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performing a phase unwrapping procedure to remove the 2π ambiguity [39], followed by an aberration compensation procedure for eliminating the phase aberrations introduced by the setup [40], the final quantitative phase image is obtained and is denoted as φx; y. For the reflection imaging mode, as shown in Fig. 2, the topography hx; y of a specimen is calculated with the following formula: hx; y
λ φx; y: 4π
(4)
4. Experimental Results
To demonstrate the feasibility of the proposed setup we conducted the phase imaging on some
nanostructured surfaces. In the first experiment a nanostructured bar etched in silicon substrate, with nominal width of 8 μm and depth of 50 nm, is used as a sample. Both the sample and the mirror, M 1 , are placed in translating stages, respectively. Once the specimen is positioned near the focal plane of microscope objective MO3 , the reference mirror M 1 is translated along the optical axis to match the OPD between the two arms, and then an optimal contrast of the hologram is achieved. Figure 3(a) shows one of the recorded off-axis holograms. The carrier frequency in Fig. 3(a) is 31.9 lines∕mm corresponding to an angle of 1.15 degrees between the filtered object and reference waves. Then, the numerical reference wave Rd is determined. Figure 3(b) shows the
Fig. 3. Measuring the results of a nanostructured silicon substrate: (a) the hologram with LED illumination; (b) Fourier spectrum of RD I; (c) topographic phase image reconstructed from (a); (d) the hologram with He–Ne laser illumination; (e) topographic phase image reconstructed from (d); (f) height profiles at the cross sections marked with dashed lines in (c) and (e). 8236
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Fig. 4. Measuring the results of a binary grating: (a) the hologram with LED illumination, fringe pattern in the inset is enlarged to view clearly; (b) topographic phase map; (c) pseudo 3D representation of the phase map in (b); (d) height profile along the white line in (b).
frequency spectrum of RD I. The spectra of object O0 R1 RD and its twin image and the DC term are separated from each other. We crop the centerlocated spectrum of the object with a circular area. The complex amplitude of the object and then the phase image can be obtained by using the described method above. After a phase unwrapping and aberration compensation procedure, the reconstructed topographic phase image calculated with Eq. (4) is shown in Fig. 3(c). For comparison of the phase noise reduction between the laser illumination and the LED illumination, we measured the specimen with the same configuration but replaced the LED with a He–Ne laser. Figure 3(d) shows one of the captured holograms with laser illumination. It clearly demonstrates that the coherent noise severely deteriorates the grade of the image. Specifically, in the bottom of the hologram lie the parasitic fringes which may come from multiple reflections in the experimental setup. Figure 3(e) shows the final topographic phase image for laser illumination. For the purpose of phase noise comparison, we select an area of the reconstructed phase image where the substrate is known to be flat, and use the standard deviation (STD) of this area as a quantitative indicator. For both illuminations, the phase noises in the same flat areas marked with white dotted rectangles in Figs. 3(c) and 3(e) are calculated, respectively. The phase noises of Fig. 3(c) and Fig. 3(e) are quantified to be 2.9 and 9.1 nm, respectively, which means that the phase noise is reduced by an order of 68% with LED illumination compared to the laser illumination. To verify the measurement accuracy of the proposed setup, height profiles along the
dashed lines across the phase images in Figs. 3(c) and 3(e) are shown in Fig. 3(f). It can be seen that both results coincide with each other, although there is a slight deviation between them, due to the phase noise. Furthermore, the height profile contains less noise for LED illumination than for laser illumination. In the second experiment, we further demonstrated the application of our proposed setup in surface topography of a microscale reflective binary grating fabricated on a silicon substrate. The captured hologram is shown in Fig. 4(a) and the unwrapped topographic phase image is shown in Fig. 4(b). Figure 4(c) also shows the result with a pseudo 3D plot. Figure 4(d) presents the height profile along the white line in Fig. 4(b). It can be seen that the measured height of the grating is about 240 nm and the period is 45 μm, which are consistent with the nominal values of the grating. The two obvious deviations, shown in Figs. 4(b) and 4(c) with the white arrows, may be caused by the defects on the grating. 5. Conclusion
In summary, we have demonstrated a new off-axis DHM scheme with a cheap LED light for illumination. The presented results demonstrate that LED light sources can suppress coherent noise significantly and render phase images with a 68% phase noise reduction. Due to the advantages of low coherent noise and high contrast ratio, we believe that the approach can provide a suitable solution in high precision industrial inspections, such as MEMS characterization, engineered surface measurement and so on. This research is supported by the Natural Science Foundation of China (NSFC) (61077005, 61107003, 1 December 2013 / Vol. 52, No. 34 / APPLIED OPTICS
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61377008). We thank Dr. Hua Liu from Xi’an technological university for providing the specimens for the experimental test. References 1. B. Kemper and G. V. Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008). 2. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999). 3. G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31, 775–777 (2006). 4. L. Yu, S. Mohanty, J. Zhang, S. Genc, M. K. Kim, M. W. Berns, and Z. Chen, “Digital holographic microscopy for quantitative cell dynamic evaluation during laser microsurgery,” Appl. Opt. 17, 12031–12038 (2009). 5. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005). 6. C. J. Mann, L. Yu, C.-M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13, 8693–8698 (2005). 7. M. T. Rinehart, N. T. Shaked, N. J. Jenness, R. L. Clark, and A. Wax, “Simultaneous two-wavelength transmission quantitative phase microscopy with a color camera,” Opt. Lett. 35, 2612–2614 (2010). 8. J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial subnanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074007 (2008). 9. S. D. Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. D. Natale, and M. Chiarini, “Surface topography of microstructures in lithium niobate by digital holographic microscopy,” Meas. Sci. Technol. 15, 961–968 (2004). 10. D. G. Abdelsalam and D. Kim, “Real-time dual-wavelength digital holographic microscopy based on polarizing separation,” Opt. Commun. 285, 233–237 (2012). 11. M. León-Rodríguez, R. Rodríguez-Vera, J. A. Rayas, and S. Calixto, “Digital holographic microscopy through a Mirau interferometric objective,” Opt. Lasers Eng. 51, 240–245 (2013). 12. L. Lovicar, J. Komrska, and R. Chmelík, “Quantitativephase-contrast imaging of two-level surface described as 2D linear filtering process,” Opt. Express 18, 20585–20594 (2010). 13. F. Charrière, J. Kühn, T. Colomb, F. Montfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, “Characterization of microlenses by digital holographic microscopy,” Appl. Opt. 45, 829–835 (2006). 14. W. J. Qu, C. O. Choo, Y. J. Yu, and A. Asundi, “Characterization and inspection of microlens array by single cube beam splitter microscopy,” Appl. Opt. 50, 886–890 (2011). 15. R. Guo, B. Yao, P. Gao, J. Min, J. Han, X. Yu, M. Lei, S. Yan, Y. Yang, D. Dan, and T. Ye, “Parallel on-axis phase-shifting holographic phase microscopy based on reflective pointdiffraction interferometer with long-term stability,” Appl. Opt. 52, 3484–3489 (2013). 16. J. Min, B. Yao, P. Gao, R. Guo, B. Ma, J. Zheng, M. Lei, S. Yan, D. Dan, T. Duan, Y. Yang, and T. Ye, “Dual-wavelength slightly off-axis digital holographic microscopy,” Appl. Opt. 51, 191–196 (2012). 17. P. Gao, B. Yao, J. Min, R. Guo, J. Zheng, T. Ye, I. Harder, V. Nercissian, and K. Mantel, “Parallel two-step phase-shifting point-diffraction interferometry for microscopy based on a pair of cube beamsplitters,” Opt. Express 19, 1930–1935 (2011). 18. F. Merola, L. Miccio, M. Paturzo, A. Finizio, S. Grilli, and P. Ferraro, “Driving and analysis of micro-objects by digital holographic microscope in microfluidics,” Opt. Lett. 36, 3079–3081 (2011). 8238
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State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China 2
Xi’an Technological University, Xi’an 710032, China *Corresponding author: [email protected]
Received 30 September 2013; revised 28 October 2013; accepted 28 October 2013; posted 29 October 2013 (Doc. ID 198529); published 25 November 2013
A reflection mode digital holographic microscope with light emitting diode (LED) illumination and offaxis interferometry is proposed. The setup is comprised of a Linnik interferometer and a grating-based 4f imaging unit. Both object and reference waves travel coaxially and are split into multiple diffraction orders in the Fourier plane by the grating. The zeroth and first orders are filtered by a polarizing array to select orthogonally polarized object waves and reference waves. Subsequently, the object and reference waves are combined again in the output plane of the 4f system, and then the hologram with uniform contrast over the entire field of view can be acquired with the aid of a polarizer. The one-shot nature in the off-axis configuration enables an interferometric recording time on a millisecond scale. The validity of the proposed setup is illustrated by imaging nanostructured substrates, and the experimental results demonstrate that the phase noise is reduced drastically by an order of 68% when compared to a He–Ne laser-based result. © 2013 Optical Society of America OCIS codes: (090.2880) Holographic interferometry; (180.3170) Interference microscopy; (120.3180) Interferometry; (120.5050) Phase measurement. http://dx.doi.org/10.1364/AO.52.008233
1. Introduction
Digital holographic microscopy (DHM) is a promising 3D imaging technology that allows the investigation of the shape of engineered surfaces or tomography of biological samples with microscale lateral resolution and nanoscale axial precision [1]. Over the past decades, thanks to newly available CCD cameras, high performance of computers, and advances in offline numerical processing techniques, DHM has been fully developed and successfully applied in diverse applications; for instance, in quantitative biology microscopy [2–7], surface relief characterization of 1559-128X/13/348233-06$15.00/0 © 2013 Optical Society of America
MEMS or other microstructures [8–12], topography of micro-optics [13–16], and so on [17–20]. Usually, coherent light sources, i.e., lasers, are adopted in DHM as illumination light, and the quality of holograms is inevitably degraded by the inherent coherent noise. When the complex object wave is numerically reconstructed from a hologram, not only is a useful phase image embedded but also phase noise (phase error) is introduced by such noises. The higher the phase noise is, the lower the measurement precision. To overcome the coherent noise, coherent lasers are replaced by light sources of partial coherence (partial temporal coherent light or partial spatial coherent light) [21–37]. Nevertheless, a light emitting diode (LED) as a light source for DHMs has not yet been fully exploited [30–37]. The principle in 1 December 2013 / Vol. 52, No. 34 / APPLIED OPTICS
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LED light source (as well as with other short time coherence light source) illuminated DHM is optical path length compensation between an object and reference arms, which is achieved by using optics pairs in both arms, as in a Michelson or a Mach– Zehnder interferometer [32–37]. However, the limited coherent length of such light sources, typically on the order of a few micrometers, hinders its application in an off-axis DHM, since just a limited number of interference fringes appear in the FOV. For this reason, temporal phase-shifting interferometry (TPSI) is more preferable, as demonstrated in most of the previous works [32–36]. Though TPSI can eliminate the direct component (DC) term and the unwanted twin image in the numerical reconstruction process, it renders some specific disadvantages when compared to the off-axis interferometry: the time resolution is low due to the need of multiple phase shifting operation; it suffers from a phase shifting error introduced by the miscalibration of the piezoelectric transducer or other phase shifting parts; and it is sensitive to the vibration caused by environmental disturbance. Recently, Dubois and Yourassowsky [37] have proposed an off-axis scheme with an LED light source, based on a Mach–Zehnder interferometer, in which a transmission grating was used to ensure an optical path difference (OPD) match between an object wave and a reference wave so that high fringe contrast was obtained in the whole FOV of the hologram. It has the advantage of one-shot full-field acquisition. However, up to three lenses were used in the reference arm for OPD compensation. It brings difficulty in the precise transverse alignment between the object and reference arms as well as increased complexity of the system. Bhaduri et al. [21] have also demonstrated the application of a halogen lamp light source in a grating-based diffraction phase interferometer. The zeroth order wave of the grating was low-pass filtered by a pin hole to generate a reference wave, whereas the first order wave passed through being untouched to act as object wave. The main limitation of this configuration is that the pinhole filtering leads to a large portion of energy loss in zeroth order beam and puts high demand on collimation of the illumination wave, which is relative a hard task for cheap LED beads. In this paper, we present an off-axis DHM with LED illumination by the use of a cheap LED bead in reflection mode, and demonstrate its application in the measurement of engineered nanostructured surfaces. The apparatus consists of two parts: a standard Linnik-type interferometer and a 4f spatial polarization filtering system. A grating is placed in conjugation with the CCD plane to provide dense interference fringes over the whole field of view. This configuration partially overcomes drawbacks presented in [21,37], i.e., only one additional objective is used for OPD match and has less energy loss, as there is no pinhole filtering, which brings convenience in optics elements alignment. The advantage 8234
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stemming from an LED light source is its low phase noise imaging capability. 2. Principal of Polarization Filtering and Experiment Setup
The scheme of the proposed polarization filtering offaxis interferometry is shown in Fig. 1(a). Two lenses, L1 and L2 , are placed in a confocal way to form a 4f imaging system. Linear grating G with period d is placed in the front focal plane of lens L1 while the CCD camera is placed in the back focal plane of lens L2 to record holograms. Vertically linearly polarized object waves and horizontally linearly polarized reference waves propagate along the optical axis and incident onto the grating G. The grating splits both the object and reference waves into multiple copies along its different diffraction orders, and different copies are separated in the Fourier plane. A polarization filter is placed at the Fourier plane to implement orthogonally polarization filtering on both the zeroth and first order waves. As depicted in Fig. 1(a), the filter consists of two rectangular opening masks; in the upper mask (has a size of 3 mm × 3 mm) a polarizer is placed with the polarization orientation parallel to that of the object wave, while in the bottom mask (has a size of 3 mm × 3 mm) a polarizer is placed with its polarization orientation perpendicular to the upper one. The zeroth order wave is filtered so that only the object wave passes, whereas the first order is filtered to pass only the reference wave. The lens L2 reshapes both the object wave and reference wave again. Polarizer P is set to convert two orthogonally polarized waves into the same polarization orientation for interference in the CCD plane. The grating is placed
Fig. 1. Polarization filtering and interference imaging: (a) schematic of 4f spatial filtering and off-axis interferometry; (b) interference fringes obtained without grating and polarization filter; (c) fringes taken with proposed scheme. Only stripes (1024 × 200 pixels) of the whole holograms are shown in (b) and (c). O and R, vertically polarized object wave and horizontally polarized reference wave, respectively; G is the, grating; L1 ∼ L2 are the lenses; P is the linear polarizer; and the polarization filter placed at the Fourier plane of lens L1 is comprised of two polarizers with orthogonal polarizations.
conjugated with the CCD plane to maintain the spatial cross correlation and the OPD match between object and reference waves [21,37]. Therefore, an interferogram with uniform contrast over the whole FOV is obtained even with reduced coherence light sources in this off-axis configuration. Figure 1(b) shows a stripe of the interferogram acquired without using the grating and the polarization filter, but just tilting the mirror M 1 [see Fig. 2] in the reference wave path. It can be seen that the fringes have uneven contrast. At the two side borders of the hologram, the contrast of fringes becomes worse. When a larger cross angle is set between the two waves, the fringe disappears rapidly. Figure 1(c) shows a same stripe size of the interferogram acquired with the grating and the polarization filtering unit. It can be seen that more dense fringes are obtained and the contrast is uniform across the entire FOV. The sketch of the experimental setup is shown in Fig. 2, which includes two parts: a Linnik-type interferometer and a 4f polarization filtering image unit. A red LED with central wavelength 630 nm and bandwidth 21 nm is used as the light source. The coherence length of the light source, 2 ln 2∕πλ2 ∕Δλ, is calculated to be 8.5 μm. The light from the LED is collimated by a telescope system comprised of a 20× microscope lens, MO1 , and a lens, L1 . A polarizer, P1 , transforms the random polarization into linear polarization. The Linnik-type interferometer consists of two identical microscope objectives, MO2 and MO3 , and two identical lenses, L2 and L3 , which are placed in symmetry to ensure OPD match between two arms. Sample S and reference mirror, M 1 , are placed in the focal planes of MO2 and MO3 , respectively. The wave reflected from mirror M 1 serves as the reference wave, whereas the wave reflected from the sample is the object wave. Polarizers P2 and P3 , with horizontal and vertical polarizations are, respectively, located in the two arms to transform the polarizations of the two waves into orthogonal polarizations. The image of the sample is projected onto the grating plane via MO3
Fig. 2. Experimental setup: NPBS is the nonpolarizing beam splitter; L1 –L5 are achromatic lenses with focal lengths of f 2 f 3 f 4 100 mm, f 5 200 mm; P1 –P4 are linear polarizers; A is the aperture; MO1 is the 20× microscope objective; MO2 and MO3 are identical microscope objectives (25×, NA 0.4); M 1 is the mirror; S is the sample; and G is a grating with period of 15 μm.
and lens L3. The object and reference waves pass through the 4f filtering image system, and then an off-axis hologram is formed in the CCD plane. The relative intensity of the two waves can be adjusted by polarizers P1 and P4 . The CCD camera has 1024 × 768 pixels, 8 bit dynamic range, and pixel size of 4.65 μm × 4.65 μm. In the setup, only the microscope objective MO2 and mirror M 1 are used for OPD match, which greatly simplifies the accurate alignment process of the setup. 3. Numerical Reconstruction
Based on the proposed setup, an off-axis interferometry for DHM is performed. We denote the unfiltered object wave as Ox; y, and the unfiltered reference wave as a constant A. For brevity of expression, we omit the influence of P4 on the amplitude of both the object and reference waves in the following expression. According to the description above, the filtered object wave O0 x; y and reference wave R1 x; y, in the CCD plane can be expressed as 1 O0 x; y a0 Ox; y ; 0
(1)
1 0 R1 x; y a1 A exp i2π x : 1 Md
(2)
Here, the subscripts denote the filtered diffraction order index. a0 and a1 are diffraction coefficients of the zeroth and the first order wave of grating G, M f 5 ∕f 4 is the magnification of the 4f image system, and x and y denote coordinates in the CCD plane. Thus, the intensity distribution of the hologram is Ix; y jO0 j2 jR1 j2 R1 O0 R1 O0 :
(3)
From Eqs. (1)–(3), we know that the hologram is a spatial modulated one with carrier frequency of 1∕Md. To suppress the DC term and the unwanted twin term, a spatial filtering technique is applied [38]. A digital reference wave RD x; y is multiplied with Ix; y, then the product RD I is Fourier transformed into the spectrum domain. The RD x; y is defined as RD x; y 1∕a1 A expi2πx∕Md, in which the carrier frequency 1∕Md can be determined from the fringe frequency of the off-axis interferogram. This manipulation shifts the spectrum of the object wave, O0 R1 RD O0 , to the original area and then it can be spatially filtered out by a low-pass digital filter mask in the spectrum domain. The complex object wave in the CCD plane can be directly obtained after an inverse Fourier transformation on the filtered spectrum. The wrapped phase image can be computed from the reconstructed complex object wave, Ox; y, given as arctanfImOx; y∕ReOx; ygmod2π. After 1 December 2013 / Vol. 52, No. 34 / APPLIED OPTICS
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performing a phase unwrapping procedure to remove the 2π ambiguity [39], followed by an aberration compensation procedure for eliminating the phase aberrations introduced by the setup [40], the final quantitative phase image is obtained and is denoted as φx; y. For the reflection imaging mode, as shown in Fig. 2, the topography hx; y of a specimen is calculated with the following formula: hx; y
λ φx; y: 4π
(4)
4. Experimental Results
To demonstrate the feasibility of the proposed setup we conducted the phase imaging on some
nanostructured surfaces. In the first experiment a nanostructured bar etched in silicon substrate, with nominal width of 8 μm and depth of 50 nm, is used as a sample. Both the sample and the mirror, M 1 , are placed in translating stages, respectively. Once the specimen is positioned near the focal plane of microscope objective MO3 , the reference mirror M 1 is translated along the optical axis to match the OPD between the two arms, and then an optimal contrast of the hologram is achieved. Figure 3(a) shows one of the recorded off-axis holograms. The carrier frequency in Fig. 3(a) is 31.9 lines∕mm corresponding to an angle of 1.15 degrees between the filtered object and reference waves. Then, the numerical reference wave Rd is determined. Figure 3(b) shows the
Fig. 3. Measuring the results of a nanostructured silicon substrate: (a) the hologram with LED illumination; (b) Fourier spectrum of RD I; (c) topographic phase image reconstructed from (a); (d) the hologram with He–Ne laser illumination; (e) topographic phase image reconstructed from (d); (f) height profiles at the cross sections marked with dashed lines in (c) and (e). 8236
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Fig. 4. Measuring the results of a binary grating: (a) the hologram with LED illumination, fringe pattern in the inset is enlarged to view clearly; (b) topographic phase map; (c) pseudo 3D representation of the phase map in (b); (d) height profile along the white line in (b).
frequency spectrum of RD I. The spectra of object O0 R1 RD and its twin image and the DC term are separated from each other. We crop the centerlocated spectrum of the object with a circular area. The complex amplitude of the object and then the phase image can be obtained by using the described method above. After a phase unwrapping and aberration compensation procedure, the reconstructed topographic phase image calculated with Eq. (4) is shown in Fig. 3(c). For comparison of the phase noise reduction between the laser illumination and the LED illumination, we measured the specimen with the same configuration but replaced the LED with a He–Ne laser. Figure 3(d) shows one of the captured holograms with laser illumination. It clearly demonstrates that the coherent noise severely deteriorates the grade of the image. Specifically, in the bottom of the hologram lie the parasitic fringes which may come from multiple reflections in the experimental setup. Figure 3(e) shows the final topographic phase image for laser illumination. For the purpose of phase noise comparison, we select an area of the reconstructed phase image where the substrate is known to be flat, and use the standard deviation (STD) of this area as a quantitative indicator. For both illuminations, the phase noises in the same flat areas marked with white dotted rectangles in Figs. 3(c) and 3(e) are calculated, respectively. The phase noises of Fig. 3(c) and Fig. 3(e) are quantified to be 2.9 and 9.1 nm, respectively, which means that the phase noise is reduced by an order of 68% with LED illumination compared to the laser illumination. To verify the measurement accuracy of the proposed setup, height profiles along the
dashed lines across the phase images in Figs. 3(c) and 3(e) are shown in Fig. 3(f). It can be seen that both results coincide with each other, although there is a slight deviation between them, due to the phase noise. Furthermore, the height profile contains less noise for LED illumination than for laser illumination. In the second experiment, we further demonstrated the application of our proposed setup in surface topography of a microscale reflective binary grating fabricated on a silicon substrate. The captured hologram is shown in Fig. 4(a) and the unwrapped topographic phase image is shown in Fig. 4(b). Figure 4(c) also shows the result with a pseudo 3D plot. Figure 4(d) presents the height profile along the white line in Fig. 4(b). It can be seen that the measured height of the grating is about 240 nm and the period is 45 μm, which are consistent with the nominal values of the grating. The two obvious deviations, shown in Figs. 4(b) and 4(c) with the white arrows, may be caused by the defects on the grating. 5. Conclusion
In summary, we have demonstrated a new off-axis DHM scheme with a cheap LED light for illumination. The presented results demonstrate that LED light sources can suppress coherent noise significantly and render phase images with a 68% phase noise reduction. Due to the advantages of low coherent noise and high contrast ratio, we believe that the approach can provide a suitable solution in high precision industrial inspections, such as MEMS characterization, engineered surface measurement and so on. This research is supported by the Natural Science Foundation of China (NSFC) (61077005, 61107003, 1 December 2013 / Vol. 52, No. 34 / APPLIED OPTICS
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