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Abstract
We report the demonstration of freeform optics metrology with an optical differentiation wavefront sensor that relies on spatially dithered distributions of binary pixels to synthesize a far-field amplitude filter. Analysis of experimental results and comparison with a commercial low-coherence-length interferometer shows that freeform phase plates with different magnitude of wavefront slopes can be accurately characterized. RMS accuracy of ∼ λ/10 and precision of ∼ λ/70 at 633 nm were achieved with pixelated filters having 2.5-µm pixels. Simulations that describe the characterization of a freeform optical component in the presence of photodetection noise and filter nonlinearity demonstrate the robustness of this wavefront-sensing approach for freeform optics characterization.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Characterizing the phase of optical waves is a crucial task in optics. Wavefront measurements in optical engineering allow for better fabrication and integration of optical components, and improvements in metrology are generally required to permit improvements in fabrication. This is particularly true for freeform optical components, i.e., non-rotationally symmetric phase components, which simultaneously require high dynamic range and high-resolution measurements [1–4].
There is a multitude of techniques to obtain quantitative phase information [5]. Interferometry converts phase information into a fluence modulation that can be measured with a square-law photodetector. Interferometers that use a reference wave, e.g., Fizeau interferometers, are the workhorses of optical testing, but they are typically limited to operation close to null testing and weak aspheres. Typical interferometric nulling components such as computer-generated holograms are part-specific, alignment sensitive, and expensive. Adaptive interferometric null test using deformable mirror and spatial light modulator have been reported for freeform metrology [6,7] but the nulling wavefront generated by a deformable mirror or spatial light modulator still needs to be precisely characterized with a high-performance wavefront sensor. Shack-Hartmann wavefront sensors (SHWS) reconstruct the test wavefront from slopes obtained by determining the centroid of far-field spots generated by an array of microlenses. The inability to correctly identify the spots generated by the different microlenses limits the dynamic range of SHWS when these spots are significantly displaced by high wavefront slopes [8]. Dynamic range extension of SHWS based on the use of liquid crystals to switch the lenslets on and off has disadvantages of light absorption, scattering and potential calibration issues [9,10]. An holographic SHWS that uses cross-correlation peak-displacement detection requires high-processing power and long processing time [11]. Sorting and phase-unwrapping based SHWS methods are limited by maximum wavefront curvature [12,13], although not by the wavefront slope. Subaperture wavefront stitching with SHWS has been investigated to overcome the dynamic range issue [14,15]. Other emerging techniques applied to freeform optical components include tilted wave interferometry [16] and low-coherence interferometry [17–19]. Although deflectometry can characterize complex shapes, it is prone to calibration errors [20,21]. Optical profilometers based on the point-cloud method can measure large size optics with high slopes [22], but the measurement time increases with resolution and size of the optics. There is still significant gain in exploring and demonstrating new wavefront-sensing technologies because of the increasing role of freeform optics and the associated metrology challenges.
In the optical differentiation wavefront sensor (ODWS), the far-field of the test wave is modulated by an amplitude filter, and the resulting near-field fluence distribution is processed to yield the wavefront gradient in one particular direction [23–25]. Two gradients in orthogonal directions are used to reconstruct the wavefront of the test wave, using algorithms identical to those developed for the SHWS. The ODWS is potentially advantageous, in particular, in terms of adjustable high dynamic range, resolution, signal-to-noise ratio and achromaticity [24,25]. It can operate in a single shot by simultaneous measurement of orthogonal gradients. We have previously reported the theoretical performance of an ODWS based on binary pixelated filters that synthesize the far-field amplitude filter via digital halftoning and presented a proof-of-concept experiment with a rotationally invariant converging lens [26]. Other ODWS demonstrations based on different implementations of the amplitude filter mostly present simulations or the qualitative detection of phase variations [23–25,27–30]. There has not been any experimental detailed demonstration of quantitative ODWS measurement of freeform optics thus far.
In this article, we demonstrate, for the first time to our knowledge, the potential of the ODWS for accurate quantitative characterization of a variety of freeform optics. Section 2 describes the ODWS principle. Section 3 presents experimental setup, design baseline, and performance evaluation in freeform optics measurements. Section 4 evaluates the effect of photodetection noise and non-ideal filter transmission profiles. Section 5 compares and contrasts the ODWS with other techniques, discusses the outlook of further ODWS investigations, and concludes this article.
2. Principle of ODWS with pixelated filters
For determination of the optical phase φ(x,y) in the near field, the ODWS relies on amplitude modulation in the far field of the optical wave under test, for example with a 4f optical system (Fig. 1).
The optical wave at the input plane is Fourier transformed by a lens to the far field, where its amplitude is modulated by a filter with linear transmission
W is the width of the filter, u and v are the spatial coordinates in the far-field plane. After Fourier transformation back to the near field, the detected fluence Fx allows for the determination of the phase slope along x usingIn this work, the wavefront is reconstructed from the two wavefront slope measurements obtained from the two orthogonal gradient filters by applying the Southwell iterative procedure [32]. Any algorithm developed for wavefront reconstruction from wavefront slopes, e.g., for Shack-Hartmann wavefront sensors, can be used, including modal reconstruction based for example on wavefront decomposition on an orthogonal basis of Zernike polynomials. The Southwell procedure was found to give excellent reconstruction on simulated and experimental data. It can operate on arbitrarily shaped apertures, and does not require the wavefront to be expandable on a particular basis, which allows for application to the widest range of wavefront metrology applications (note for example that the freeform phase plates used in this experimental demonstration have a manufacturing artifact that is poorly fitted by the low-order modes). To account for any static aberration present in the optical system, a reference wavefront without test element is first measured, then subtracted from all test wavefronts.
Accurately synthesizing a spatially varying transmission filter is not a simple task. Already published ODWS demonstrations include the use of a liquid crystal spatial light modulator (SLM) [33,34], spatially varying optical activity [35] and holographic film [36]. SLM-based filters are both wavelength and polarization dependent and may have undesirable diffraction orders. Spatially varying optical activity is also wavelength-sensitive and requires fabrication of a custom optical component. Holographic film might not have the optical quality required for accurate wavefront reconstruction. In our recent work [26], we have used spatially dithered distributions of transparent and opaque pixels to synthesize the transmission profile of an ODWS filter [37]. The high-frequency noise from pixelation and binarization is pushed away from the optical axis as the pixel size decreases, i.e., away from the camera’s field of view, resulting in accurate implementation of the amplitude filter [26]. These components are achromatic and can be fabricated at large aperture and low cost by commercial lithography of a metal layer deposited on a glass substrate.
3. Experiments and results
3.1 Measurement configuration
The ODWS setup is shown in Fig. 2. A 20-mm collimated laser beam (λ = 633 nm) propagates through a test phase plate. The image-relay system (focal lengths of 750 mm and 125 mm) down collimates the beam by a factor of 6.1. The field is Fourier transformed by the first lens of a 4f system (f = 1 m) to a Fourier plane where the gradient transmission filter is located. After amplitude modulation, the field is Fourier transformed back by the second lens and the resulting fluence is finally detected by a CCD camera. It is noted that, down collimation does not change the Peak-To-Valley (PV) and Root Mean Square (RMS) of the wavefront. However, the wavefront slope increases proportionally to the down-collimation factor. The resolution of the ODWS measurement at the phase plate location is 26.7 µm, corresponding to the camera pixel resolution of 4.4 µm. The camera has an 8-bit analog-to-digital converter, but its signal-to-noise ratio, including detection noise, is of the order of 84.
Spatially dithered amplitude filters with field transmission changing linearly between 0 and 1 over the width W = 10 mm were designed using the standard four-weight error diffusion algorithm [38]. Although filters with pixels size ranging from 2.5 µm to 10 µm have been manufactured and tested, the experimental results presented in this article were obtained with the 2.5-µm filter because we have shown that the ODWS accuracy increases with decreasing pixel size of binary filter [39]. Although the 2.5-µm filter has the highest nonlinearity relative to the ideal ODWS-filter profile (see Section 4), it was experimentally found that it yields better retrieval in practice because of lower pixelation noise.
3.2 Design baseline and performance-evaluation method
The ODWS presented in the previous section has a dynamic range equal to ∼ 16 waves/mm, corresponding to ∼ 20 µm/mm surface slope at 633-nm wavelength. The bias point in our experiment is the center of the filter, hence the range of wavefront slopes that can be measured is [-8, +8] waves/mm [36].
To assess the performance of the ODWS, we have characterized one rotationally symmetric phase plate (Sec. 3.3) and three freeform phase plates (Sec. 3.4 and 3.5). The freeform phase plates (thereafter referenced to as #1, #2, and #3) were designed to have horizontal coma of different amplitude over a 20-mm aperture to investigate the ODWS performance over a range of wavefront slopes, but due to manufacturing error, contain power and other aberrations. The corresponding range of wavefront slopes at the conjugate plane of phase plates in waves/mm are [-3.4, 1.9], [-11.1, 3.7] and [-5.5, 19.3]. The wavefront slopes of the first two phase plates are either within or slightly exceeding the ODWS design baseline and that of third phase plate is higher than the design baseline.
The four phase plates were fabricated with UltraForm [40] at OptiPro Systems. These parts were characterized with an UltraSurf (OptiPro Systems) metrology system, a computer controlled non-contact coordinate measuring machine which is based on low-coherence interferometry [22]. Characterizing the freeform phase plates with a Zygo interferometer (Zygo GPI 4” Verifier AT) in transmission mode without any nulling component was successful for phase plate #1, but was not successful for phase plates #2 and #3, which would therefore require the manufacturing of specific nulling components. We therefore used the residual errors between ODWS and UltraSurf measurements to validate the ODWS measurements. It should be noted that this error contains the inherent error in both the ODWS and UltraSurf measurements, as well as imperfect registration (translation and rotation) between the reconstructed wavefronts, magnification and other experimental imperfection. For all wavefronts, piston, tip, and tilt were removed, as is customary in the metrology of optical components.
3.3 ODWS measurement validation using a rotationally symmetric optics
The ODWS was first compared to the UltraSurf when characterizing a rotationally symmetric optics. The UltraSurf measurement is shown in Fig. 3(a). Figure 3(b) shows the wavefront result as an average of 20 sets of measurements by the ODWS. The validity is determined by calculating the RMS of difference between the measured wavefronts. The difference is shown in Fig. 3(c) and the measurements agree to 0.08λ.
Fig. 3. Wavefront of a rotationally symmetric optics (a) measured with UltraSurf, RMS = 0.18λ, PV = 0.8λ; (b) measured with ODWS, RMS = 0.19λ, PV = 0.8λ (c) difference, RMS = 0.08λ.
3.4 Demonstration of wavefront measurement of freeform phase plates
In this section we present and compare the transmission wavefront measured by the ODWS, the UltraSurf and the Zygo interferometer for freeform phase plates #1 and #2. The wavefront of phase plate #1 measured by UltraSurf and ODWS are shown in Figs. 4(a) and 4(b) respectively, and the difference of the two measurements is shown in Fig. 4(c). A similar comparison between Zygo interferometer and ODWS measurement for phase plate #1 is shown in Fig. 5. Similarly, the measurement results of phase plate #2 are shown in Fig. 6. The ODWS wavefront result is obtained by averaging the measurements performed on four different days, each having 10 measurements. Piston, tip/tilt were removed due to the reasons mentioned in Section 3.2. The feature located at the center of each phase plate, which is retrieved by the three diagnostics, is a manufacturing artifact. From the difference maps shown in Figs. 4(c), 5(c) and 6(c), the wavefront measured on phase plates #1 and #2 by the ODWS are comparable to the wavefront measured by other techniques. The corresponding RMS of the wavefront difference is 0.04λ (phase plate #1, ODWS/UltraSurf), 0.06λ (phase plate #1, ODWS/Zygo) and 0.1λ (phase plate #2, ODWS/UltraSurf). For reference, the RMS of the wavefront difference calculated with the Zygo and UltraSurf wavefront maps for phase plate #1 is 0.05λ, showing that even the wavefront returned by the two commercial diagnostics are not identical.
Fig. 4. Wavefront of freeform phase plate #1 (a) measured with UltraSurf, RMS = 0.16λ, PV = 0.86λ; (b) measured with ODWS, RMS = 0.15λ, PV = 0.79λ; (c) difference, RMS = 0.04λ
Fig. 5. Wavefront of freeform phase plate #1 (a) measured with Zygo interferometer, RMS = 0.2λ, PV = 0.87λ; (b) measured with ODWS, RMS = 0.15λ, PV = 0.79λ; (c) difference RMS = 0.06λ.
Fig. 6. Wavefront of freeform phase plate #2 (a) measured with UltraSurf, RMS = 0.38λ, PV = 2.58λ; (b) measured with ODWS, RMS = 0.39λ, PV = 2.28λ; (c) difference RMS = 0.1λ.
To illustrate the measurement for the freeform component of the wavefront, we removed the power term from the ODWS measurements shown in Figs. 4(b) and 6(b) and show the results in Figs. 7(a) and 7(b) for phase plate #1 and #2, respectively. The primary coma aberration is more clearly visible after the power removal, although the plotted wavefronts still include higher-order aberrations and the sharp central feature.
Fig. 7. Wavefront measured by the ODWS after power removal for (a) freeform phase plate #1; RMS = 0.06λ, PV = 0.38λ; (b) freeform phase plate #2; RMS = 0.16λ, PV = 1.13λ.
The measurement precision was quantified by taking the RMS difference between individual wavefront maps and the average of multiple measurements on each day. Figure 8 shows an average precision of 0.014λ for phase plate #2, using data taken over four consecutive days. The maximum variation between measurements is 0.02λ at worst which shows that the measurements are highly consistent. The observed precision is impacted not only by detection noise but also by environmental factors such as air turbulence in the laboratory environment. Because this ODWS implementation is based on fluence measurements that are sequentially measured, the measurement precision could be improved using a stabilized laser source and a high-dynamic-range camera.
Fig. 8. Precision plot for 40 measurements of phase plate #2 taken over four days, average precision is 0.014λ.
3.5 Impact of filter width on high wavefront slope measurement
High wavefront slopes leading to far-field components beyond the 1-cm filter width are not expected to be accurately measured, leading to poor wavefront reconstruction at the corresponding near-field locations. The purpose of this section is to experimentally investigate this effect. For this study, we choose phase plate #3 which has wavefront slopes much higher than the theoretical limitation of the current ODWS design. The maximum wavefront slope resides near the left edge of the phase plate with an aperture of 20 mm. Because the portion of the beam that has larger wavefront slope lands closer to the edge of the filter, we compare wavefront measurements over two apertures with diameter equal to 15 mm and 20 mm, respectively. The ranges of wavefront slopes at the conjugate plane are within ([-5.5, 6.3] waves/mm for the 15-mm diameter) and much beyond ([-5.5, 19.3] waves/mm for the 20-mm diameter) the dynamic range design baseline for the implemented ODWS ([-8, 8] waves/mm, corresponding to the 1-cm filter width).
The wavefront maps of phase plate #3 in the 15 mm pupil are shown in Figs. 9(a) and 9(b). Owing to the fact that maximum wavefront slope at 15-mm aperture is within the design baseline of the implemented 1-cm filter, the ODWS and UltraSurf measurements agree well, within 0.1λ RMS [Fig. 9(c)]. The Zernike coefficients (in fringe Zernike order) for these two measurements are in excellent agreement [Fig. 10]. The Zernike coefficients are obtained by fitting 37 Zernike polynomials, with terms 4 to 15 shown in Fig. 10. We note that the bump at the center of the wavefront is poorly fitted by Zernike polynomials, potentially leading to discrepancies.
Fig. 9. Wavefront of freeform phase plate #3 within 15-mm aperture (a) measured with UltraSurf, RMS = 0.66λ, PV = 2.8λ; (b) measured with ODWS, RMS = 0.59λ, PV = 2.61λ; (c) difference, RMS = 0.1λ.
When increasing the pupil size from 15 mm to 20 mm, the high wavefront slopes at the left edge of this phase plate exceed theoretical limit of the implemented ODWS ([-5.5, 19.3] vs. [-8, 8] waves/mm). The RMS difference of the measurements by UltraSurf and ODWS subsequently increases from 0.1λ to 0.16λ [Fig. 9(c) and Fig. 11(c)].
Fig. 11. Wavefront of freeform phase plate #3 within 20 mm (a) measured with UltraSurf, RMS = 0.69λ, PV = 4.44λ; (b) measured with ODWS, RMS = 0.6λ, PV = 2.8λ; (c) absolute difference, RMS = 0.16λ.
In Fig. 11(c), the highest difference between the two measurements is observed at the left edge in the difference map (plotted as magnitude of the difference to emphasize the peak value on the left side of the aperture). This can be explained by fluence measurements performed in the far-field plane, where the ODWS filter is located, and in the detection plane, where the near-field fluence is measured. Figure 12(a) shows the far-field of phase plate #3 compared to the 1-cm filter width. The high-slope wavefront components that exceed the design baseline are clipped by the filter at the right edge, marked with a white line. This far-field clipping results in a dark patch at the left edge in the fluence map of phase plate #3 at the detection plane as shown in Fig. 12(b). The resulting dark patch in fluence distribution due to clipping from the current filter-width design leads to less accurate wavefront reconstruction in that region, although good wavefront reconstruction is observed everywhere else.
Fig. 12. Fluence at far-field plane for (a) phase plate #3 and (c) phase plate #2, and at the detection plane for (b) phase plate #3 and (d) phase plate #2. All data is measured with a filter having 100% transmission over 1 cm. On (a) and (c), the ODWS-filter 1-cm width is shown by two white lines. On (b) and (d), the 20 mm measurement diameter is indicated by a white circle. The PSF images are intentionally saturated towards the center to make the edge visible.
We further demonstrate that this far-field clipping is the main source of inaccurate wavefront retrieval. Figures 12(c) and 12(d) show the measurement results through the same filter for phase plate #2 that has wavefront slopes close to the design baseline. The lower wavefront slopes lead to smaller spatial spread of the far field, well within the filter width. The wavefronts measured by the ODWS and the UltraSurf agree within 0.1λ RMS [Fig. 6(c)]
These results experimentally confirm that the ODWS dynamic range is effectively limited by filter width, because far-field components induced beyond that by large wavefront slopes lead to inaccurate wavefront reconstruction. One possible way to improve the dynamic range is to increase the filter width. Another way is to decrease the far-field size below the filter width by decreasing the focal length of the 4f optical system. However, in the latter case, the far field is sampled by fewer filter pixels, leading to less accurate wavefront reconstruction [26]. This can be alleviated, to some extent, by using smaller pixels, although this might be practically limited by manufacturing fabrication requirements.
Characterization of phase plate #3 with the Zygo interferometer was not successful as some portion in the center and on the edge of the wavefront could not be retrieved due to high slopes there. A raw wavefront returned by the software is displayed in Fig. 13, showing areas where the wavefront was not reconstructed and set to NaN (Not a Number), same as background. The measurement has a resolution of 51.4 µm for a 22 mm measurement aperture.
4. Simulation study for impact of experimental imperfection and choice of optimal filter
4.1 Simulations description
The effect of experimental imperfections was simulated by considering an ODWS based on a 4f line with f = 1 m and detection with a camera having 7.7-µm pixels. This pixel size, which is set by simulation sampling requirements in the near field and far field, is close to the experimental pixel size (4.4 µm) and typical of scientific cameras. A wave with uniform fluence and phase given by a test wavefront is propagated to the far field, modulated by the filter transmission, and Fourier transformed back to the near field for detection. The fluences in the x and y direction are simulated, then used for wavefront reconstruction using the Southwell procedure. The test wavefronts correspond to Alvarez lens profiles proportional to x3/3 + xy2 [41], with the quoted amplitude being the maximal amplitude over the 1-cm-diameter pupil. For a 1-wave amplitude, the largest wavefront slope is approximately 0.78 waves/mm in both the x and y direction over the 1-cm pupil. This indicates that the accuracy of an ideal ODWS is expected be excellent for these test wavefronts until their amplitude reaches approximately 10 waves, leading to wavefront slopes equal to DR/2 (8 waves/mm), for which some light in the far field reaches the edge of the filter.
4.2 Effect of detection noise
Additive uncorrelated noise with standard deviation s normalized to the value of Fx and Fy for a flat input wavefront was introduced on all pixels of the two detected fluences Fx and Fy. Figure 14 shows the RMS error on the retrieved wavefront as a function of the test-wavefront amplitude for various values of s. It is clear that the ODWS can tolerate high levels of noise. The main effect of the detection noise is to decrease the dynamic range. In the absence of noise (s = 0), the RMS error increases sharply for large wavefront amplitudes which lead to energy at the edge of the far-field filter. When detection noise is present, the RMS error increases for low-amplitude test wavefronts. This is however a minor effect, considering that the largest noise level considered in these simulations (s = 10%) is much larger than the typical noise of modern scientific cameras. For comparison, the RMS error obtained with three ideal pixelated binary filters (pixel size equal to 10 µm, 5 µm, and 2.5 µm) and noise-free detection has been plotted on the same figure. It is clear that noise due to filters with large pixels is the dominant factor limiting the accuracy for wavefront amplitudes approximately smaller than 5 waves, while photodetection noise becomes dominant beyond that. The induced errors remain below λ/20 over the ODWS dynamic range.
Fig. 14. Calculated RMS error for the reconstructed wavefront of an Alvarez lens of varying amplitude for various noise levels from 0% to 10% and an ideal continuous filter (continuous lines). The RMS errors corresponding to noise-free detection with ideal pixelated filters (10 µm, 5 µm, and 2.5 µm) are indicated with markers.
4.3. Effect of non-ideal filter transmission profile
We simulate the performance impact of the non-ideal filter transmission profile arising from fabrication uncertainties by two different approaches. The transmission profile (Eq. (1)) was first modified using the following analytical formula:
Fig. 15. Calculated RMS error for the reconstructed wavefront of an Alvarez lens of varying amplitude for various nonlinearity coefficient q and an ideal continuous filter (continuous lines) and for the measured transmission profiles of the pixelated filters (markers).
We then fitted the measured transmission profiles of the three fabricated filters (pixel size equal to 10 µm, 5 µm, and 2.5 µm) with fourth-order polynomials to remove the noise associated with the transmission measurement and facilitate interpolation in the simulations. The determined polynomials were used to generate filter transmission profiles in the wavefront reconstruction simulations. Owing to the fact that filters are non-ideal, the field transmission is not linear over the filter width W, and the transmission slope is not uniformly equal to 1/W over the ODWS dynamic range. To compensate for this effect in the phase retrieval from the calculated Fx and Fy, the quantity W in Eqs. (2) and (3) was replaced by the inverse of the measured filter slope at u = 0. Using this effective slope compensates for the non-ideal filter transmission for wavefronts leading to far fields that are contained within the region where the filter transmission is linear with the identified slope. The simulated RMS reconstruction (Fig. 15) shows that the larger transmission profile error associated with smaller pixels leads to larger phase-retrieval error. While smaller pixels lead in theory to better accuracy because of lower noise due to pixelation, transmission profile errors due to fabrication tolerance increase for smaller pixels. Comparison of Figs. 14 and 15 shows that the 2.5-µm filter is the optimal choice for wavefront smaller than a few waves, but the profile error leads to relatively larger measurement error for that pixel size than for larger pixel sizes for larger wavefronts. Reconstruction error smaller than λ/10 is achievable with the current filters, which were fabricated with a mild tolerance of +/-0.5 µm, over most of the ODWS dynamic range. Improving the accuracy and taking advantage of the smaller pixel size over the full dynamic range of the ODWS requires tighter fabrication tolerance to limit the transmission profile error to within a few percent. Digital halftoning algorithms generating pixel distributions that are less sensitive to fabrication errors could also be investigated [42].
5. Discussion and conclusion
The main advantages of the ODWS are its adjustable high dynamic range and high spatial resolution. The resolution and dynamic range of a Shack-Hartmann sensor are limited by the lenslet array. Taking as an example a commercial Shack-Hartmann sensor (WFS20-5C, Thorlabs), the lenslet size (146 µm) and focal length (41 mm) allow for measuring wavefront slopes up to approximately 28 waves/mm without the use of advanced hardware or processing techniques. With a focal length of 1 m, a wavelength of 633 nm and a filter width equal to 10 cm, which is achievable with commercial lithography fabrication techniques, the calculated ODWS dynamic range is of the order of 158 waves/mm. The ODWS dynamic range can be improved by increasing the filter width or decreasing the focal length. Though coordinate based techniques can measure high surface slopes, ODWS has the advantage of short measurement times. Coordinate-based measurements typically have micron-level precision and recent point cloud based metrology has achieved λ/14 precision [43]. This ODWS demonstration has shown precision of λ/70 that is comparable to nanometer level precision in interferometry. Various techniques used to increase the dynamic range of metrology techniques, for example sub-aperture stitching, can readily be implemented with an ODWS. Finally, the ODWS can be used with a source at different wavelengths, and does not require a high-coherence source.
We have demonstrated the first high-performance optical differentiation wavefront sensor based on spatially dithered binary pixelated filters towards freeform metrology. Its performance in freeform phase plate measurement is compared to that of a commercial scanning low-coherence interferometer, showing excellent agreement. The accuracy in comparison and precision have been determined to be ∼ λ/10 (RMS) and ∼ λ/70 (RMS), respectively. We experimentally demonstrated that the dynamic range can be increased via tailoring the filter width or focal length of the imaging system. Simulations that include the photodetection noise and the far-field filter nonlinearity demonstrate the impact of these parameters and the general robustness of the ODWS.
Work is underway to make the ODWS measurement single-shot by acquiring the two orthogonal wavefront gradients simultaneously. We are also working on improving the sensitivity simultaneously with the dynamic range by implementing different filter transmission profiles [30,44], for which the amplitude control demonstrated with spatially dithered pixel distributions would be beneficial. The lithography process used to manufacture the spatially dithered filters is compatible with filter sizes much larger than what has been used here (1 cm). Filters with larger width will be implemented to measure stronger freeforms.
Funding
National Science Foundation (EPMD 1711669).
Acknowledgments
We thank Scott DeFisher at OptiPro Systems (Rochester, NY, USA) for helpful discussions, for manufacturing the phase plates and measuring their surface profiles using an UltraSurf. We thank Dr. Feng Tao for useful technical discussions about this work. We thank the Robert E. Hopkins Center for Optical Design and Engineering at the University of Rochester for providing access to a Zygo interferometer.
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