Artificial Intelligence/Machine Learning, Army STTR, Phase I
Zernike Polynomials via Phase Recovery
Objective
The Army needs a technology that can completely characterize an optic under test via phase recovery and a collimated, partially-coherent light source.
Description
Developing this capability will enable enhanced resolution in the Army’s ubiquitous, direct-view optical systems. This advancement will also improve Soldier survivability and lethality due to increased situational awareness and greater ability to detect, classify, recognize and identify threats.
The United States Army needs to characterize optical systems to validate their design and performance. Commercial systems can measure the modulation transfer function, effective focal length, field curvature and distortion. These systems monitor the Fourier transform plane of the lens under test.
However, current commercial systems are unable to extract coma and spherical aberrations. Hopkins or Seidel coefficients that pertain to ray traces do not form an orthonormal basis. In comparison, the Zernike polynomials are a proper basis that describe wavefront error. Frame captures contain only intensity information and recovering the Zernike coefficients requires phase recovery.
Brady (2005) and Fienup (1993) characterized the Hubble Space Telescope using a variation of the Gerchberg-Saxton algorithm (Wittle, 2018). Phase recovery is an inverse problem and requires constraints. Normally, one uses two planes: the image plane and the Fourier transform plane. However, other methods work, including the use of a series of frames to capture data about the Fourier Transform plane (Dube, 2018; Zhou, 2021; Gureyev, 2004); Mehrabkhani, 2017; Volkov, 2001).
The Army assumes Pinhole illumination in advance. This would be near the effective focal length of the lens under test. Because this is near the waist of the caustic, there is a concern as to how much (Fisher) information is available. Thus, the auxiliary planes must be near the region of maximum curvature for the caustic. In the far field, one can use the Fraunhofer approximate for the more general Huygen-Fresnel (H-F) propagator. Whether or not a Fresnel approximation is valid may depend upon the f-number of the LUT.
The acquisition of off-axis terms will require that the lens be rotated about its second nodal point. This is also true for interferometric approaches (Gates, 1955; ZYGO). The rotation of the LUT also satisfies the conditions outlined in Zhou (2021). As implemented, it is a form of tomography. The Army is not interested in compressive sensing (Candes, 2011; Li, 2020), nor any other solution that requires the addition of optical elements (Fuerschbach, 2014) such as phase screens or beam splitters into the optical path this topic. The Army also expects the aberrated Airy disk to be commercially examined via a microscope objective and image sensing array.
Phase I
Vendors must develop the algorithms needed for implementing phase recovery using a series of planes near the location of the Fourier transform plane of the LUT. Businesses must demonstrate that the algorithm can converge to solutions consistent with those derived from interferometric methods. Vendors need to determine the criteria for setting the spacing between these planes for the best performance.
Phase II
Using the results from Phase I, vendors should develop the hardware and software needed to realize the procedure on a commercial system. Businesses can manually enter plane locations to offload image processing.
Phase III
Vendors must make the necessary hardware and software adjustments to a commercial platform, automate the acquisition procedure and automate the extraction of the Zernike polynomials.
Submission Information
All eligible businesses must submit proposals by noon ET.
To view full solicitation details, click here.
For more information, and to submit your full proposal package, visit the DSIP Portal.
STTR Help Desk: usarmy.rtp.devcom-arl.mbx.sttr-pmo@army.mil
References:
- Brady (2005), Gregory R. and James R. Fienup; “Phase retrieval as an optical metrology tool”; In Optifab 2005: Technical Digest (Vol. 10315, pp. 143-145). SPIE. Proceedings of SPIE – The International Society for Optical Engineering. 10.1117/12.605914.
- Candes (2011), Emmanuel J., Thomas Strohmer and Vladislav Veroninski; “PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming”; arXiv:1109.4499v1 [cs.IT] 21 Sep 2011.
- Dube (2018), Brandon D. “On the Use of Classical MTF Measurements to Perform Wavefront Sensing”; Thesis, The Institute of Optics Hajim School of Engineering and Applied Sciences; https://www.retrorefractions.com/pdf/bdd_ug_thesis_10.pdf
- Fienup (1993), James R.; “Phase-retrieval algorithms for a complicated optical system”. Applied optics, 32 10, 1737-46.
- Fuerschbach (2014), Kyle, Kevin P. Thompson, and Jannick P. Rolland; Interferometric measurement of a concave, φ-polynomial, Zernike mirror”; Optics Letters / Vol. 39, No. 1 / January 1, 2014.
- Gureyev (2004), T.E.; A Pogany, D.M Paganin, S.W Wilkins, “Linear algorithms for phase retrieval in the Fresnel region”; Optics Communications,Vol. 231; Issues 1–6, Pp. 53-70,; ISSN 0030-4018,; https://doi.org/10.1016/j.optcom.2003.12.020.
- Li (2020) Fanxing, Wei Yan, , Fupin Peng, Simo Wang and Jialin Du; “Enhanced Phase Retrieval Method Based on Random Phase Modulation”; Appl. Sci. 2020, 10, 1184; doi:10.3390/app10031184
- Mehrabkhani (2017), Soheil & Kuester, Melvin. “Optimization of phase retrieval in the Fresnel domain by the modified Gerchberg-Saxton algorithm”; https://arxiv.org/ftp/arxiv/papers/1711/1711.01176.pdf
- Volkov (2001), V., & Zhu, Y.; “Phase Retrieval from Two Defocused Images by the Transport-Ofintensity Equation Formalism with Fast Fourier Transform”. Microscopy and Microanalysis, 7(S2), 430-431 Aug. 5-9 Long Beach CA; doi:10.1017/S1431927600028221
- Wittle (2018), Lily. Investigating the Gerchberg-Saxton Phase Retrieval Algorithm. SIAM Undergraduate Research Online. 11. 10.1137/17S016610.
- Zhou (2021) Guocheng, Shaohui Zhang, Yayu Zhai, Yao Hu, Qun Hao; “Single-Shot Through-Focus Image Acquisition and Phase Retrieval from Chromatic Aberration and Multi-Angle Illumination”; Frontiers in Physics, vol.9; DOI=10.3389/fphy.2021.648827 https://www.frontiersin.org/articles/10.3389/fphy.2021.648827
- ZYGO “Typical Interferometer Setups”; https://www.zygo.com/-/media/project/ameteksxa/zygo/ametekzygo/downloadables/brochures/interferometers/typical-interferometer-setups.pdf]
- Phase Recovery, Zernike Polynomials, Fresnel Propagator, Inverse problem, Constraints, Priors.
Objective
The Army needs a technology that can completely characterize an optic under test via phase recovery and a collimated, partially-coherent light source.
Description
Developing this capability will enable enhanced resolution in the Army’s ubiquitous, direct-view optical systems. This advancement will also improve Soldier survivability and lethality due to increased situational awareness and greater ability to detect, classify, recognize and identify threats.
The United States Army needs to characterize optical systems to validate their design and performance. Commercial systems can measure the modulation transfer function, effective focal length, field curvature and distortion. These systems monitor the Fourier transform plane of the lens under test.
However, current commercial systems are unable to extract coma and spherical aberrations. Hopkins or Seidel coefficients that pertain to ray traces do not form an orthonormal basis. In comparison, the Zernike polynomials are a proper basis that describe wavefront error. Frame captures contain only intensity information and recovering the Zernike coefficients requires phase recovery.
Brady (2005) and Fienup (1993) characterized the Hubble Space Telescope using a variation of the Gerchberg-Saxton algorithm (Wittle, 2018). Phase recovery is an inverse problem and requires constraints. Normally, one uses two planes: the image plane and the Fourier transform plane. However, other methods work, including the use of a series of frames to capture data about the Fourier Transform plane (Dube, 2018; Zhou, 2021; Gureyev, 2004); Mehrabkhani, 2017; Volkov, 2001).
The Army assumes Pinhole illumination in advance. This would be near the effective focal length of the lens under test. Because this is near the waist of the caustic, there is a concern as to how much (Fisher) information is available. Thus, the auxiliary planes must be near the region of maximum curvature for the caustic. In the far field, one can use the Fraunhofer approximate for the more general Huygen-Fresnel (H-F) propagator. Whether or not a Fresnel approximation is valid may depend upon the f-number of the LUT.
The acquisition of off-axis terms will require that the lens be rotated about its second nodal point. This is also true for interferometric approaches (Gates, 1955; ZYGO). The rotation of the LUT also satisfies the conditions outlined in Zhou (2021). As implemented, it is a form of tomography. The Army is not interested in compressive sensing (Candes, 2011; Li, 2020), nor any other solution that requires the addition of optical elements (Fuerschbach, 2014) such as phase screens or beam splitters into the optical path this topic. The Army also expects the aberrated Airy disk to be commercially examined via a microscope objective and image sensing array.
Phase I
Vendors must develop the algorithms needed for implementing phase recovery using a series of planes near the location of the Fourier transform plane of the LUT. Businesses must demonstrate that the algorithm can converge to solutions consistent with those derived from interferometric methods. Vendors need to determine the criteria for setting the spacing between these planes for the best performance.
Phase II
Using the results from Phase I, vendors should develop the hardware and software needed to realize the procedure on a commercial system. Businesses can manually enter plane locations to offload image processing.
Phase III
Vendors must make the necessary hardware and software adjustments to a commercial platform, automate the acquisition procedure and automate the extraction of the Zernike polynomials.
Submission Information
All eligible businesses must submit proposals by noon ET.
To view full solicitation details, click here.
For more information, and to submit your full proposal package, visit the DSIP Portal.
STTR Help Desk: usarmy.rtp.devcom-arl.mbx.sttr-pmo@army.mil
References:
- Brady (2005), Gregory R. and James R. Fienup; “Phase retrieval as an optical metrology tool”; In Optifab 2005: Technical Digest (Vol. 10315, pp. 143-145). SPIE. Proceedings of SPIE – The International Society for Optical Engineering. 10.1117/12.605914.
- Candes (2011), Emmanuel J., Thomas Strohmer and Vladislav Veroninski; “PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming”; arXiv:1109.4499v1 [cs.IT] 21 Sep 2011.
- Dube (2018), Brandon D. “On the Use of Classical MTF Measurements to Perform Wavefront Sensing”; Thesis, The Institute of Optics Hajim School of Engineering and Applied Sciences; https://www.retrorefractions.com/pdf/bdd_ug_thesis_10.pdf
- Fienup (1993), James R.; “Phase-retrieval algorithms for a complicated optical system”. Applied optics, 32 10, 1737-46.
- Fuerschbach (2014), Kyle, Kevin P. Thompson, and Jannick P. Rolland; Interferometric measurement of a concave, φ-polynomial, Zernike mirror”; Optics Letters / Vol. 39, No. 1 / January 1, 2014.
- Gureyev (2004), T.E.; A Pogany, D.M Paganin, S.W Wilkins, “Linear algorithms for phase retrieval in the Fresnel region”; Optics Communications,Vol. 231; Issues 1–6, Pp. 53-70,; ISSN 0030-4018,; https://doi.org/10.1016/j.optcom.2003.12.020.
- Li (2020) Fanxing, Wei Yan, , Fupin Peng, Simo Wang and Jialin Du; “Enhanced Phase Retrieval Method Based on Random Phase Modulation”; Appl. Sci. 2020, 10, 1184; doi:10.3390/app10031184
- Mehrabkhani (2017), Soheil & Kuester, Melvin. “Optimization of phase retrieval in the Fresnel domain by the modified Gerchberg-Saxton algorithm”; https://arxiv.org/ftp/arxiv/papers/1711/1711.01176.pdf
- Volkov (2001), V., & Zhu, Y.; “Phase Retrieval from Two Defocused Images by the Transport-Ofintensity Equation Formalism with Fast Fourier Transform”. Microscopy and Microanalysis, 7(S2), 430-431 Aug. 5-9 Long Beach CA; doi:10.1017/S1431927600028221
- Wittle (2018), Lily. Investigating the Gerchberg-Saxton Phase Retrieval Algorithm. SIAM Undergraduate Research Online. 11. 10.1137/17S016610.
- Zhou (2021) Guocheng, Shaohui Zhang, Yayu Zhai, Yao Hu, Qun Hao; “Single-Shot Through-Focus Image Acquisition and Phase Retrieval from Chromatic Aberration and Multi-Angle Illumination”; Frontiers in Physics, vol.9; DOI=10.3389/fphy.2021.648827 https://www.frontiersin.org/articles/10.3389/fphy.2021.648827
- ZYGO “Typical Interferometer Setups”; https://www.zygo.com/-/media/project/ameteksxa/zygo/ametekzygo/downloadables/brochures/interferometers/typical-interferometer-setups.pdf]
- Phase Recovery, Zernike Polynomials, Fresnel Propagator, Inverse problem, Constraints, Priors.