Abstract

Wavefront sensing with a thin diffuser has emerged as a potential low-cost alternative to a lenslet array for aberrometry. Here we show that displacement of caustic patterns can be tracked for estimating wavefront gradient in a diffuser wavefront sensor (DWFS), enabling large dynamic-range wavefront measurements with sufficient accuracy for eyeglass prescription measurements. We compare the dynamic range, repeatability, precision, and number of resolvable prescriptions of a DWFS to a Shack-Hartmann wavefront sensor (SHWFS) for autorefraction measurement. We induce spherical and cylindrical errors in a model eye and use a multi-level Demon’s non-rigid registration algorithm to estimate caustic displacements relative to an emmetropic model eye. When compared to spherical error measurements with the SHWFS using a laser diode with a laser speckle reducer, the DWFS demonstrates a ∼5-fold improvement in dynamic range (−4.0 to +4.5 D vs. −22.0 to +19.5 D) with less than half the reduction in resolution (0.072 vs. 0.116 D), enabling a ∼3-fold increase in the number of resolvable prescriptions (118 vs. 358). In addition to being lower-cost, the unique, non-periodic nature of the caustic pattern formed by a diffuser enables a larger dynamic range of aberration measurements compared to a lenslet array.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

2017 (2)

2016 (1)

2015 (6)

Y. Saita, H. Shinto, and T. Nomura, “Holographic Shack–Hartmann wavefront sensor based on the correlation peak displacement detection method for wavefront sensing with large dynamic range,” Optica 2, 411–415 (2015).
[Crossref]

N. J. Durr, S. R. Dave, F. A. Vera-Diaz, D. Lim, C. Dorronsoro, S. Marcos, F. Thorn, and E. Lage, “Design and Clinical Evaluation of a Handheld Wavefront Autorefractor,” Optom. Vis. Sci. 92, 1140–1147 (2015).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref]

A. S. Goncharov, N. G. Iroshnikov, A. V. Larichev, and I. P. Nikolaev, “The impact of speckle on the measurement of eye aberrations,” J. Mod. Opt. 62, 1775–1780 (2015).
[Crossref]

A. Yousef, J. Li, and M. Karim, “High-speed image registration algorithm with subpixel accuracy,” IEEE Signal Process. Lett. 22, 1796–1800 (2015).
[Crossref]

2014 (5)

R. Applegate, D. Atchison, A. Bradley, A. Bruce, M. Collins, J. Marsack, S. Read, L. N. Thibos, and G. Yoon, “Wavefront Refraction and Correction,” Optom. Vis. Sci. 91, 1154–1155 (2014).
[Crossref]

A. S. Bruce and L. J. Catania, “Clinical Applications of Wavefront Refraction,” Optom. Vis. Sci. 91, 1278–1286 (2014).
[Crossref] [PubMed]

N. J. Durr, S. R. Dave, E. Lage, S. Marcos, F. Thorn, and D. Lim, “From Unseen to Seen: Tackling the Global Burden of Uncorrected Refractive Errors,” Annu. Rev. Biomed. Eng. 16, 131–153 (2014).
[Crossref] [PubMed]

Optotune, “Laser speckle reduction with Optotune’s laser speckle reducer LSR-3000 & LSR-OEM,” Appl. Note 20141–14 (2014).

L. Yu, M. Xia, H. Xie, L. Xuan, and J. Ma, “Novel methods to improve the measurement accuracy and the dynamic range of Shack–Hartmann wavefront sensor,” J. Mod. Opt. 61, 909054 (2014).
[Crossref]

2012 (3)

K. S. Naidoo and J. Jaggernath, “Uncorrected refractive errors,” Indian J. Ophthalmol. 60, 432–437 (2012).
[Crossref] [PubMed]

T. R. Fricke, B. A. Holden, D. A. Wilson, G. Schlenther, K. S. Naidoo, S. Resnikoff, and K. D. Frick, “Global cost of correcting vision impairment from uncorrected refractive error,” Bull. World Heal. Organ. 90, 728–738 (2012).
[Crossref]

S. Resnikoff, W. Felch, T.-M. Gauthier, and B. Spivey, “The number of ophthalmologists in practice and training worldwide: a growing gap despite more than 200,000 practitioners,” Br. J. Ophthalmol. 96, 783–787 (2012).
[Crossref] [PubMed]

2010 (2)

V. F. Pamplona, A. Mohan, M. M. Oliveira, and R. Raskar, “NETRA : Interactive Display for Estimating Refractive Errors and Focal Range,” Assoc. for Comput. Mach. (ACM) 4, 77(2010).

M. Xia, C. Li, L. Hu, Z. Cao, Q. Mu, and L. Xuan, “Shack-Hartmann wavefront sensor with large dynamic range,” J. Biomed. Opt. 15(2), 1–10 (2010).
[Crossref]

2009 (3)

C. Leroux and C. Dainty, “A simple and robust method to extend the dynamic range of an aberrometer,” Opt. Express 17, 19055–19061 (2009).
[Crossref]

T. S. T. Smith, K. D. Frick, B. A. Holden, T. R. Fricke, and K. S. Naidoo, “Potential lost productivity resulting from the global burden of uncorrected refractive error,” Bull. World Heal. Organ. 87, 431–437 (2009).
[Crossref]

C. E. Campbell, “The range of local wavefront curvatures measurable with Shack-Hartmann wavefront sensors,” Clin. Exp. Optom. 92, 187–193 (2009).
[Crossref] [PubMed]

2008 (2)

S. Resnikoff, D. Pascolini, S. P. Mariotti, and G. P. Pokharel, “Global magnitude of visual impairment caused by uncorrected refractive errors in 2004,” Bull. World Heal. Organ. 86 (1), 63–70 (2008).
[Crossref]

Y. Hongbin, Z. Guangya, C. F. Siong, and L. Feiwen, “A tunable Shack–Hartmann wavefront sensor based on a liquid-filled microlens array,” J. Micromechanics Microengineering 18, 1–8 (2008).
[Crossref]

2007 (1)

S.-H. Baik, S. K. Park, C.-J. Kim, and B. Cha, “A center detection algorithm for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 39, 262–267 (2007).
[Crossref]

2004 (1)

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

2003 (1)

X. Cheng, N. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a Clinical Shack-Hartmann Aberrometer,” Optom. Vis. Sci. 80, 587–595 (2003).
[Crossref] [PubMed]

2001 (2)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[Crossref] [PubMed]

R. Dandona and L. Dandona, “Refractive error blindness,” Bull. World Heal. Organ. 79, 237–243 (2001).

1998 (2)

J. P. Thirion, “Image matching as a diffusion process: An analogy with Maxwell’s demons,” Med. Image Analysis 2, 243–260 (1998).
[Crossref]

J. Pfund, N. Lindlein, and J. Schwider, “Dynamic range expansion of a Shack–Hartmann sensor by use of a modified unwrapping algorithm,” Opt. Lett. 23, 995–997 (1998).
[Crossref]

1997 (1)

L. N. Thibos, W. Wheeler, and D. Horner, “Power Vectors: An Application of Fourier Analysis to the Descriptive and Statistical Analysis of Refractive Error,” Optom. Vis. Sci. 74, 367–375 (1997).
[Crossref] [PubMed]

1995 (1)

D. Atchison, A. Bradley, L. N. Thibos, and G. Smith, “Useful Variations of the Badal Optometer,” Am. Acad. Optom. 72, 279–284 (1995).
[Crossref]

1994 (1)

J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. 11, 1949–1957 (1994).
[Crossref]

1988 (3)

S. Wittenberg, “The Badal Optometer Paradox,” Am. Acad. Optom. 65, 285–291 (1988).
[Crossref]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref] [PubMed]

I. Freund, M. Rosenbluh, and S. Feng, “Memory Effects in Propagation of Optical Waves through Disordered Media,” Phys. Rev. Lett. 61, 2328–2332 (1988).
[Crossref] [PubMed]

Antipa, N.

N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “DiffuserCam: lensless single-exposure 3D imaging,” Optica 5, 1–9 (2018).
[Crossref]

N. Antipa, S. Necula, R. Ng, and L. Waller, “Single-Shot Diffuser-Encoded Light Field Imaging,” in IEEE International Conference on Computational Photography, (IEEE, 2016).

Applegate, R.

R. Applegate, D. Atchison, A. Bradley, A. Bruce, M. Collins, J. Marsack, S. Read, L. N. Thibos, and G. Yoon, “Wavefront Refraction and Correction,” Optom. Vis. Sci. 91, 1154–1155 (2014).
[Crossref]

Applegate, R. A.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

Atchison, D.

R. Applegate, D. Atchison, A. Bradley, A. Bruce, M. Collins, J. Marsack, S. Read, L. N. Thibos, and G. Yoon, “Wavefront Refraction and Correction,” Optom. Vis. Sci. 91, 1154–1155 (2014).
[Crossref]

D. Atchison, A. Bradley, L. N. Thibos, and G. Smith, “Useful Variations of the Badal Optometer,” Am. Acad. Optom. 72, 279–284 (1995).
[Crossref]

Awwal, A.

J. Porter, H. M. Queener, J. E. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science. Principles, Practices, Design, and Applications (John Wiley & Sons, Inc., 2006).
[Crossref]

Baik, S.-H.

S.-H. Baik, S. K. Park, C.-J. Kim, and B. Cha, “A center detection algorithm for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 39, 262–267 (2007).
[Crossref]

Bao, Y.

P. M. Cumberland, Y. Bao, P. G. Hysi, P. J. Foster, C. J. Hammond, J. S. Rahi, and U. B. E. &. V. Consortium, “Frequency and Distribution of Refractive Error in Adult Life: Methodology and Findings of the UK Biobank Study,” PLOS ONE 10, 1–14 (2015).
[Crossref]

Berto, P.

Bille, J. F.

J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. 11, 1949–1957 (1994).
[Crossref]

Bostan, E.

Bradley, A.

R. Applegate, D. Atchison, A. Bradley, A. Bruce, M. Collins, J. Marsack, S. Read, L. N. Thibos, and G. Yoon, “Wavefront Refraction and Correction,” Optom. Vis. Sci. 91, 1154–1155 (2014).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

X. Cheng, N. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a Clinical Shack-Hartmann Aberrometer,” Optom. Vis. Sci. 80, 587–595 (2003).
[Crossref] [PubMed]

D. Atchison, A. Bradley, L. N. Thibos, and G. Smith, “Useful Variations of the Badal Optometer,” Am. Acad. Optom. 72, 279–284 (1995).
[Crossref]

Bruce, A.

R. Applegate, D. Atchison, A. Bradley, A. Bruce, M. Collins, J. Marsack, S. Read, L. N. Thibos, and G. Yoon, “Wavefront Refraction and Correction,” Optom. Vis. Sci. 91, 1154–1155 (2014).
[Crossref]

Bruce, A. S.

A. S. Bruce and L. J. Catania, “Clinical Applications of Wavefront Refraction,” Optom. Vis. Sci. 91, 1278–1286 (2014).
[Crossref] [PubMed]

Campbell, C. E.

C. E. Campbell, “The range of local wavefront curvatures measurable with Shack-Hartmann wavefront sensors,” Clin. Exp. Optom. 92, 187–193 (2009).
[Crossref] [PubMed]

Cao, Z.

M. Xia, C. Li, L. Hu, Z. Cao, Q. Mu, and L. Xuan, “Shack-Hartmann wavefront sensor with large dynamic range,” J. Biomed. Opt. 15(2), 1–10 (2010).
[Crossref]

Catania, L. J.

A. S. Bruce and L. J. Catania, “Clinical Applications of Wavefront Refraction,” Optom. Vis. Sci. 91, 1278–1286 (2014).
[Crossref] [PubMed]

Cha, B.

S.-H. Baik, S. K. Park, C.-J. Kim, and B. Cha, “A center detection algorithm for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 39, 262–267 (2007).
[Crossref]

Cheng, X.

X. Cheng, N. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a Clinical Shack-Hartmann Aberrometer,” Optom. Vis. Sci. 80, 587–595 (2003).
[Crossref] [PubMed]

Ciuffreda, K. J.

K. J. Ciuffreda and M. Rosenfield, “Evaluation of the SVOne: A Handheld, Smartphone-Based Autorefractor,” Optom. Vis. Sci. 92, 1133–1139 (2015).
[Crossref] [PubMed]

Collins, M.

R. Applegate, D. Atchison, A. Bradley, A. Bruce, M. Collins, J. Marsack, S. Read, L. N. Thibos, and G. Yoon, “Wavefront Refraction and Correction,” Optom. Vis. Sci. 91, 1154–1155 (2014).
[Crossref]

Cumberland, P. M.

P. M. Cumberland, Y. Bao, P. G. Hysi, P. J. Foster, C. J. Hammond, J. S. Rahi, and U. B. E. &. V. Consortium, “Frequency and Distribution of Refractive Error in Adult Life: Methodology and Findings of the UK Biobank Study,” PLOS ONE 10, 1–14 (2015).
[Crossref]

Dai, G.-M.

G.-M. Dai, Wavefront Optics for Vision Correction (Bellingham, Walsh, 2008).
[Crossref]

Dainty, C.

Dandona, L.

R. Dandona and L. Dandona, “Refractive error blindness,” Bull. World Heal. Organ. 79, 237–243 (2001).

Dandona, R.

R. Dandona and L. Dandona, “Refractive error blindness,” Bull. World Heal. Organ. 79, 237–243 (2001).

Dave, S. R.

N. J. Durr, S. R. Dave, F. A. Vera-Diaz, D. Lim, C. Dorronsoro, S. Marcos, F. Thorn, and E. Lage, “Design and Clinical Evaluation of a Handheld Wavefront Autorefractor,” Optom. Vis. Sci. 92, 1140–1147 (2015).
[Crossref] [PubMed]

N. J. Durr, S. R. Dave, E. Lage, S. Marcos, F. Thorn, and D. Lim, “From Unseen to Seen: Tackling the Global Burden of Uncorrected Refractive Errors,” Annu. Rev. Biomed. Eng. 16, 131–153 (2014).
[Crossref] [PubMed]

N. J. Durr, S. R. Dave, D. Lim, S. Joseph, T. D. Ravilla, and E. Lage, “Quality of eyeglass prescriptions from a low-cost wavefront autorefractor evaluated in rural India: results of a 708-participant field study.” bioRxiv (2018).

Dorronsoro, C.

N. J. Durr, S. R. Dave, F. A. Vera-Diaz, D. Lim, C. Dorronsoro, S. Marcos, F. Thorn, and E. Lage, “Design and Clinical Evaluation of a Handheld Wavefront Autorefractor,” Optom. Vis. Sci. 92, 1140–1147 (2015).
[Crossref] [PubMed]

Durr, N. J.

N. J. Durr, S. R. Dave, F. A. Vera-Diaz, D. Lim, C. Dorronsoro, S. Marcos, F. Thorn, and E. Lage, “Design and Clinical Evaluation of a Handheld Wavefront Autorefractor,” Optom. Vis. Sci. 92, 1140–1147 (2015).
[Crossref] [PubMed]

N. J. Durr, S. R. Dave, E. Lage, S. Marcos, F. Thorn, and D. Lim, “From Unseen to Seen: Tackling the Global Burden of Uncorrected Refractive Errors,” Annu. Rev. Biomed. Eng. 16, 131–153 (2014).
[Crossref] [PubMed]

N. J. Durr, S. R. Dave, D. Lim, S. Joseph, T. D. Ravilla, and E. Lage, “Quality of eyeglass prescriptions from a low-cost wavefront autorefractor evaluated in rural India: results of a 708-participant field study.” bioRxiv (2018).

Feiwen, L.

Y. Hongbin, Z. Guangya, C. F. Siong, and L. Feiwen, “A tunable Shack–Hartmann wavefront sensor based on a liquid-filled microlens array,” J. Micromechanics Microengineering 18, 1–8 (2008).
[Crossref]

Felch, W.

S. Resnikoff, W. Felch, T.-M. Gauthier, and B. Spivey, “The number of ophthalmologists in practice and training worldwide: a growing gap despite more than 200,000 practitioners,” Br. J. Ophthalmol. 96, 783–787 (2012).
[Crossref] [PubMed]

Feng, S.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref] [PubMed]

I. Freund, M. Rosenbluh, and S. Feng, “Memory Effects in Propagation of Optical Waves through Disordered Media,” Phys. Rev. Lett. 61, 2328–2332 (1988).
[Crossref] [PubMed]

Foster, P. J.

P. M. Cumberland, Y. Bao, P. G. Hysi, P. J. Foster, C. J. Hammond, J. S. Rahi, and U. B. E. &. V. Consortium, “Frequency and Distribution of Refractive Error in Adult Life: Methodology and Findings of the UK Biobank Study,” PLOS ONE 10, 1–14 (2015).
[Crossref]

Freund, I.

I. Freund, M. Rosenbluh, and S. Feng, “Memory Effects in Propagation of Optical Waves through Disordered Media,” Phys. Rev. Lett. 61, 2328–2332 (1988).
[Crossref] [PubMed]

Frick, K. D.

T. R. Fricke, B. A. Holden, D. A. Wilson, G. Schlenther, K. S. Naidoo, S. Resnikoff, and K. D. Frick, “Global cost of correcting vision impairment from uncorrected refractive error,” Bull. World Heal. Organ. 90, 728–738 (2012).
[Crossref]

T. S. T. Smith, K. D. Frick, B. A. Holden, T. R. Fricke, and K. S. Naidoo, “Potential lost productivity resulting from the global burden of uncorrected refractive error,” Bull. World Heal. Organ. 87, 431–437 (2009).
[Crossref]

Fricke, T. R.

T. R. Fricke, B. A. Holden, D. A. Wilson, G. Schlenther, K. S. Naidoo, S. Resnikoff, and K. D. Frick, “Global cost of correcting vision impairment from uncorrected refractive error,” Bull. World Heal. Organ. 90, 728–738 (2012).
[Crossref]

T. S. T. Smith, K. D. Frick, B. A. Holden, T. R. Fricke, and K. S. Naidoo, “Potential lost productivity resulting from the global burden of uncorrected refractive error,” Bull. World Heal. Organ. 87, 431–437 (2009).
[Crossref]

Gauthier, T.-M.

S. Resnikoff, W. Felch, T.-M. Gauthier, and B. Spivey, “The number of ophthalmologists in practice and training worldwide: a growing gap despite more than 200,000 practitioners,” Br. J. Ophthalmol. 96, 783–787 (2012).
[Crossref] [PubMed]

Goelz, S.

J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. 11, 1949–1957 (1994).
[Crossref]

Goncharov, A. S.

A. S. Goncharov, N. G. Iroshnikov, A. V. Larichev, and I. P. Nikolaev, “The impact of speckle on the measurement of eye aberrations,” J. Mod. Opt. 62, 1775–1780 (2015).
[Crossref]

Grimm, B.

J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. 11, 1949–1957 (1994).
[Crossref]

Guangya, Z.

Y. Hongbin, Z. Guangya, C. F. Siong, and L. Feiwen, “A tunable Shack–Hartmann wavefront sensor based on a liquid-filled microlens array,” J. Micromechanics Microengineering 18, 1–8 (2008).
[Crossref]

Guillon, M.

Gunjala, G.

Hammond, C. J.

P. M. Cumberland, Y. Bao, P. G. Hysi, P. J. Foster, C. J. Hammond, J. S. Rahi, and U. B. E. &. V. Consortium, “Frequency and Distribution of Refractive Error in Adult Life: Methodology and Findings of the UK Biobank Study,” PLOS ONE 10, 1–14 (2015).
[Crossref]

Heckel, R.

Himebaugh, N.

X. Cheng, N. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a Clinical Shack-Hartmann Aberrometer,” Optom. Vis. Sci. 80, 587–595 (2003).
[Crossref] [PubMed]

Holden, B. A.

T. R. Fricke, B. A. Holden, D. A. Wilson, G. Schlenther, K. S. Naidoo, S. Resnikoff, and K. D. Frick, “Global cost of correcting vision impairment from uncorrected refractive error,” Bull. World Heal. Organ. 90, 728–738 (2012).
[Crossref]

T. S. T. Smith, K. D. Frick, B. A. Holden, T. R. Fricke, and K. S. Naidoo, “Potential lost productivity resulting from the global burden of uncorrected refractive error,” Bull. World Heal. Organ. 87, 431–437 (2009).
[Crossref]

Hong, X.

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

Hongbin, Y.

Y. Hongbin, Z. Guangya, C. F. Siong, and L. Feiwen, “A tunable Shack–Hartmann wavefront sensor based on a liquid-filled microlens array,” J. Micromechanics Microengineering 18, 1–8 (2008).
[Crossref]

Horner, D.

L. N. Thibos, W. Wheeler, and D. Horner, “Power Vectors: An Application of Fourier Analysis to the Descriptive and Statistical Analysis of Refractive Error,” Optom. Vis. Sci. 74, 367–375 (1997).
[Crossref] [PubMed]

Hrynchak, P. K.

E. L. Irving, C. M. Machan, S. Lam, P. K. Hrynchak, and L. Lillakas, “Refractive error magnitude and variability: Relation to age,” J. Optom. 12, 55–63 (2018).
[Crossref] [PubMed]

Hu, L.

M. Xia, C. Li, L. Hu, Z. Cao, Q. Mu, and L. Xuan, “Shack-Hartmann wavefront sensor with large dynamic range,” J. Biomed. Opt. 15(2), 1–10 (2010).
[Crossref]

Huang, G.

G. Huang, H. Jiang, K. Matthews, and P. Wilford, “Lensless Imaging by Compressive Sensing,” IEEE ICIP pp. 2101–2105 (2013).

Hysi, P. G.

P. M. Cumberland, Y. Bao, P. G. Hysi, P. J. Foster, C. J. Hammond, J. S. Rahi, and U. B. E. &. V. Consortium, “Frequency and Distribution of Refractive Error in Adult Life: Methodology and Findings of the UK Biobank Study,” PLOS ONE 10, 1–14 (2015).
[Crossref]

Iroshnikov, N. G.

A. S. Goncharov, N. G. Iroshnikov, A. V. Larichev, and I. P. Nikolaev, “The impact of speckle on the measurement of eye aberrations,” J. Mod. Opt. 62, 1775–1780 (2015).
[Crossref]

Irving, E. L.

E. L. Irving, C. M. Machan, S. Lam, P. K. Hrynchak, and L. Lillakas, “Refractive error magnitude and variability: Relation to age,” J. Optom. 12, 55–63 (2018).
[Crossref] [PubMed]

Jaggernath, J.

K. S. Naidoo and J. Jaggernath, “Uncorrected refractive errors,” Indian J. Ophthalmol. 60, 432–437 (2012).
[Crossref] [PubMed]

Jiang, H.

G. Huang, H. Jiang, K. Matthews, and P. Wilford, “Lensless Imaging by Compressive Sensing,” IEEE ICIP pp. 2101–2105 (2013).

Joseph, S.

N. J. Durr, S. R. Dave, D. Lim, S. Joseph, T. D. Ravilla, and E. Lage, “Quality of eyeglass prescriptions from a low-cost wavefront autorefractor evaluated in rural India: results of a 708-participant field study.” bioRxiv (2018).

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref] [PubMed]

Karim, M.

A. Yousef, J. Li, and M. Karim, “High-speed image registration algorithm with subpixel accuracy,” IEEE Signal Process. Lett. 22, 1796–1800 (2015).
[Crossref]

Kim, C.-J.

S.-H. Baik, S. K. Park, C.-J. Kim, and B. Cha, “A center detection algorithm for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 39, 262–267 (2007).
[Crossref]

Kollbaum, P. S.

X. Cheng, N. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a Clinical Shack-Hartmann Aberrometer,” Optom. Vis. Sci. 80, 587–595 (2003).
[Crossref] [PubMed]

Kuo, G.

Lage, E.

N. J. Durr, S. R. Dave, F. A. Vera-Diaz, D. Lim, C. Dorronsoro, S. Marcos, F. Thorn, and E. Lage, “Design and Clinical Evaluation of a Handheld Wavefront Autorefractor,” Optom. Vis. Sci. 92, 1140–1147 (2015).
[Crossref] [PubMed]

N. J. Durr, S. R. Dave, E. Lage, S. Marcos, F. Thorn, and D. Lim, “From Unseen to Seen: Tackling the Global Burden of Uncorrected Refractive Errors,” Annu. Rev. Biomed. Eng. 16, 131–153 (2014).
[Crossref] [PubMed]

N. J. Durr, S. R. Dave, D. Lim, S. Joseph, T. D. Ravilla, and E. Lage, “Quality of eyeglass prescriptions from a low-cost wavefront autorefractor evaluated in rural India: results of a 708-participant field study.” bioRxiv (2018).

Lam, S.

E. L. Irving, C. M. Machan, S. Lam, P. K. Hrynchak, and L. Lillakas, “Refractive error magnitude and variability: Relation to age,” J. Optom. 12, 55–63 (2018).
[Crossref] [PubMed]

Larichev, A. V.

A. S. Goncharov, N. G. Iroshnikov, A. V. Larichev, and I. P. Nikolaev, “The impact of speckle on the measurement of eye aberrations,” J. Mod. Opt. 62, 1775–1780 (2015).
[Crossref]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref] [PubMed]

Leroux, C.

Li, C.

M. Xia, C. Li, L. Hu, Z. Cao, Q. Mu, and L. Xuan, “Shack-Hartmann wavefront sensor with large dynamic range,” J. Biomed. Opt. 15(2), 1–10 (2010).
[Crossref]

Li, J.

A. Yousef, J. Li, and M. Karim, “High-speed image registration algorithm with subpixel accuracy,” IEEE Signal Process. Lett. 22, 1796–1800 (2015).
[Crossref]

Liang, J.

J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. 11, 1949–1957 (1994).
[Crossref]

Liang, Z.

Lillakas, L.

E. L. Irving, C. M. Machan, S. Lam, P. K. Hrynchak, and L. Lillakas, “Refractive error magnitude and variability: Relation to age,” J. Optom. 12, 55–63 (2018).
[Crossref] [PubMed]

Lim, D.

N. J. Durr, S. R. Dave, F. A. Vera-Diaz, D. Lim, C. Dorronsoro, S. Marcos, F. Thorn, and E. Lage, “Design and Clinical Evaluation of a Handheld Wavefront Autorefractor,” Optom. Vis. Sci. 92, 1140–1147 (2015).
[Crossref] [PubMed]

N. J. Durr, S. R. Dave, E. Lage, S. Marcos, F. Thorn, and D. Lim, “From Unseen to Seen: Tackling the Global Burden of Uncorrected Refractive Errors,” Annu. Rev. Biomed. Eng. 16, 131–153 (2014).
[Crossref] [PubMed]

N. J. Durr, S. R. Dave, D. Lim, S. Joseph, T. D. Ravilla, and E. Lage, “Quality of eyeglass prescriptions from a low-cost wavefront autorefractor evaluated in rural India: results of a 708-participant field study.” bioRxiv (2018).

Lin, J. E.

J. Porter, H. M. Queener, J. E. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science. Principles, Practices, Design, and Applications (John Wiley & Sons, Inc., 2006).
[Crossref]

Lindlein, N.

Ma, J.

L. Yu, M. Xia, H. Xie, L. Xuan, and J. Ma, “Novel methods to improve the measurement accuracy and the dynamic range of Shack–Hartmann wavefront sensor,” J. Mod. Opt. 61, 909054 (2014).
[Crossref]

Machan, C. M.

E. L. Irving, C. M. Machan, S. Lam, P. K. Hrynchak, and L. Lillakas, “Refractive error magnitude and variability: Relation to age,” J. Optom. 12, 55–63 (2018).
[Crossref] [PubMed]

Marcos, S.

N. J. Durr, S. R. Dave, F. A. Vera-Diaz, D. Lim, C. Dorronsoro, S. Marcos, F. Thorn, and E. Lage, “Design and Clinical Evaluation of a Handheld Wavefront Autorefractor,” Optom. Vis. Sci. 92, 1140–1147 (2015).
[Crossref] [PubMed]

N. J. Durr, S. R. Dave, E. Lage, S. Marcos, F. Thorn, and D. Lim, “From Unseen to Seen: Tackling the Global Burden of Uncorrected Refractive Errors,” Annu. Rev. Biomed. Eng. 16, 131–153 (2014).
[Crossref] [PubMed]

Mariotti, S. P.

S. Resnikoff, D. Pascolini, S. P. Mariotti, and G. P. Pokharel, “Global magnitude of visual impairment caused by uncorrected refractive errors in 2004,” Bull. World Heal. Organ. 86 (1), 63–70 (2008).
[Crossref]

Marsack, J.

R. Applegate, D. Atchison, A. Bradley, A. Bruce, M. Collins, J. Marsack, S. Read, L. N. Thibos, and G. Yoon, “Wavefront Refraction and Correction,” Optom. Vis. Sci. 91, 1154–1155 (2014).
[Crossref]

Matthews, K.

G. Huang, H. Jiang, K. Matthews, and P. Wilford, “Lensless Imaging by Compressive Sensing,” IEEE ICIP pp. 2101–2105 (2013).

Mildenhall, B.

Mohan, A.

V. F. Pamplona, A. Mohan, M. M. Oliveira, and R. Raskar, “NETRA : Interactive Display for Estimating Refractive Errors and Focal Range,” Assoc. for Comput. Mach. (ACM) 4, 77(2010).

Mu, Q.

M. Xia, C. Li, L. Hu, Z. Cao, Q. Mu, and L. Xuan, “Shack-Hartmann wavefront sensor with large dynamic range,” J. Biomed. Opt. 15(2), 1–10 (2010).
[Crossref]

Naidoo, K. S.

T. R. Fricke, B. A. Holden, D. A. Wilson, G. Schlenther, K. S. Naidoo, S. Resnikoff, and K. D. Frick, “Global cost of correcting vision impairment from uncorrected refractive error,” Bull. World Heal. Organ. 90, 728–738 (2012).
[Crossref]

K. S. Naidoo and J. Jaggernath, “Uncorrected refractive errors,” Indian J. Ophthalmol. 60, 432–437 (2012).
[Crossref] [PubMed]

T. S. T. Smith, K. D. Frick, B. A. Holden, T. R. Fricke, and K. S. Naidoo, “Potential lost productivity resulting from the global burden of uncorrected refractive error,” Bull. World Heal. Organ. 87, 431–437 (2009).
[Crossref]

Necula, S.

N. Antipa, S. Necula, R. Ng, and L. Waller, “Single-Shot Diffuser-Encoded Light Field Imaging,” in IEEE International Conference on Computational Photography, (IEEE, 2016).

Ng, R.

N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “DiffuserCam: lensless single-exposure 3D imaging,” Optica 5, 1–9 (2018).
[Crossref]

N. Antipa, S. Necula, R. Ng, and L. Waller, “Single-Shot Diffuser-Encoded Light Field Imaging,” in IEEE International Conference on Computational Photography, (IEEE, 2016).

Nikolaev, I. P.

A. S. Goncharov, N. G. Iroshnikov, A. V. Larichev, and I. P. Nikolaev, “The impact of speckle on the measurement of eye aberrations,” J. Mod. Opt. 62, 1775–1780 (2015).
[Crossref]

Nomura, T.

Oliveira, M. M.

V. F. Pamplona, A. Mohan, M. M. Oliveira, and R. Raskar, “NETRA : Interactive Display for Estimating Refractive Errors and Focal Range,” Assoc. for Comput. Mach. (ACM) 4, 77(2010).

Pamplona, V. F.

V. F. Pamplona, A. Mohan, M. M. Oliveira, and R. Raskar, “NETRA : Interactive Display for Estimating Refractive Errors and Focal Range,” Assoc. for Comput. Mach. (ACM) 4, 77(2010).

Park, S. K.

S.-H. Baik, S. K. Park, C.-J. Kim, and B. Cha, “A center detection algorithm for Shack-Hartmann wavefront sensor,” Opt. Laser Technol. 39, 262–267 (2007).
[Crossref]

Pascolini, D.

S. Resnikoff, D. Pascolini, S. P. Mariotti, and G. P. Pokharel, “Global magnitude of visual impairment caused by uncorrected refractive errors in 2004,” Bull. World Heal. Organ. 86 (1), 63–70 (2008).
[Crossref]

Pfund, J.

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[Crossref] [PubMed]

Pokharel, G. P.

S. Resnikoff, D. Pascolini, S. P. Mariotti, and G. P. Pokharel, “Global magnitude of visual impairment caused by uncorrected refractive errors in 2004,” Bull. World Heal. Organ. 86 (1), 63–70 (2008).
[Crossref]

Porter, J.

J. Porter, H. M. Queener, J. E. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science. Principles, Practices, Design, and Applications (John Wiley & Sons, Inc., 2006).
[Crossref]

Queener, H. M.

J. Porter, H. M. Queener, J. E. Lin, K. Thorn, and A. Awwal, Adaptive Optics for Vision Science. Principles, Practices, Design, and Applications (John Wiley & Sons, Inc., 2006).
[Crossref]

Rahi, J. S.

P. M. Cumberland, Y. Bao, P. G. Hysi, P. J. Foster, C. J. Hammond, J. S. Rahi, and U. B. E. &. V. Consortium, “Frequency and Distribution of Refractive Error in Adult Life: Methodology and Findings of the UK Biobank Study,” PLOS ONE 10, 1–14 (2015).
[Crossref]

Raskar, R.

V. F. Pamplona, A. Mohan, M. M. Oliveira, and R. Raskar, “NETRA : Interactive Display for Estimating Refractive Errors and Focal Range,” Assoc. for Comput. Mach. (ACM) 4, 77(2010).

Ravilla, T. D.

N. J. Durr, S. R. Dave, D. Lim, S. Joseph, T. D. Ravilla, and E. Lage, “Quality of eyeglass prescriptions from a low-cost wavefront autorefractor evaluated in rural India: results of a 708-participant field study.” bioRxiv (2018).

Read, S.

R. Applegate, D. Atchison, A. Bradley, A. Bruce, M. Collins, J. Marsack, S. Read, L. N. Thibos, and G. Yoon, “Wavefront Refraction and Correction,” Optom. Vis. Sci. 91, 1154–1155 (2014).
[Crossref]

Resnikoff, S.

S. Resnikoff, W. Felch, T.-M. Gauthier, and B. Spivey, “The number of ophthalmologists in practice and training worldwide: a growing gap despite more than 200,000 practitioners,” Br. J. Ophthalmol. 96, 783–787 (2012).
[Crossref] [PubMed]

T. R. Fricke, B. A. Holden, D. A. Wilson, G. Schlenther, K. S. Naidoo, S. Resnikoff, and K. D. Frick, “Global cost of correcting vision impairment from uncorrected refractive error,” Bull. World Heal. Organ. 90, 728–738 (2012).
[Crossref]

S. Resnikoff, D. Pascolini, S. P. Mariotti, and G. P. Pokharel, “Global magnitude of visual impairment caused by uncorrected refractive errors in 2004,” Bull. World Heal. Organ. 86 (1), 63–70 (2008).
[Crossref]

Rigneault, H.

Rosenbluh, M.

I. Freund, M. Rosenbluh, and S. Feng, “Memory Effects in Propagation of Optical Waves through Disordered Media,” Phys. Rev. Lett. 61, 2328–2332 (1988).
[Crossref] [PubMed]

Rosenfield, M.

K. J. Ciuffreda and M. Rosenfield, “Evaluation of the SVOne: A Handheld, Smartphone-Based Autorefractor,” Optom. Vis. Sci. 92, 1133–1139 (2015).
[Crossref] [PubMed]

Saita, Y.

Schlenther, G.

T. R. Fricke, B. A. Holden, D. A. Wilson, G. Schlenther, K. S. Naidoo, S. Resnikoff, and K. D. Frick, “Global cost of correcting vision impairment from uncorrected refractive error,” Bull. World Heal. Organ. 90, 728–738 (2012).
[Crossref]

Schwider, J.

Schwiegerling, J.

J. Schwiegerling, Field Guide to Visual and Ophthalmic Optics (SPIE Press, 2004).
[Crossref]

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[Crossref] [PubMed]

Shanker, A.

Sherwin, S.

Shinto, H.

Siong, C. F.

Y. Hongbin, Z. Guangya, C. F. Siong, and L. Feiwen, “A tunable Shack–Hartmann wavefront sensor based on a liquid-filled microlens array,” J. Micromechanics Microengineering 18, 1–8 (2008).
[Crossref]

Smith, G.

D. Atchison, A. Bradley, L. N. Thibos, and G. Smith, “Useful Variations of the Badal Optometer,” Am. Acad. Optom. 72, 279–284 (1995).
[Crossref]

Smith, T. S. T.

T. S. T. Smith, K. D. Frick, B. A. Holden, T. R. Fricke, and K. S. Naidoo, “Potential lost productivity resulting from the global burden of uncorrected refractive error,” Bull. World Heal. Organ. 87, 431–437 (2009).
[Crossref]

Song, L.

Spivey, B.

S. Resnikoff, W. Felch, T.-M. Gauthier, and B. Spivey, “The number of ophthalmologists in practice and training worldwide: a growing gap despite more than 200,000 practitioners,” Br. J. Ophthalmol. 96, 783–787 (2012).
[Crossref] [PubMed]

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and Fluctuations of Coherent Wave Transmission through Disordered Media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref] [PubMed]

Su, L.

Thibos, L. N.

R. Applegate, D. Atchison, A. Bradley, A. Bruce, M. Collins, J. Marsack, S. Read, L. N. Thibos, and G. Yoon, “Wavefront Refraction and Correction,” Optom. Vis. Sci. 91, 1154–1155 (2014).
[Crossref]

L. N. Thibos, X. Hong, A. Bradley, and R. A. Applegate, “Accuracy and precision of objective refraction from wavefront aberrations,” J. Vis. 4, 9 (2004).
[Crossref]

X. Cheng, N. Himebaugh, P. S. Kollbaum, L. N. Thibos, and A. Bradley, “Validation of a Clinical Shack-Hartmann Aberrometer,” Optom. Vis. Sci. 80, 587–595 (2003).
[Crossref] [PubMed]

L. N. Thibos, W. Wheeler, and D. Horner, “Power Vectors: An Application of Fourier Analysis to the Descriptive and Statistical Analysis of Refractive Error,” Optom. Vis. Sci. 74, 367–375 (1997).
[Crossref] [PubMed]

D. Atchison, A. Bradley, L. N. Thibos, and G. Smith, “Useful Variations of the Badal Optometer,” Am. Acad. Optom. 72, 279–284 (1995).
[Crossref]

Thirion, J. P.

J. P. Thirion, “Image matching as a diffusion process: An analogy with Maxwell’s demons,” Med. Image Analysis 2, 243–260 (1998).
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Figures (12)

Fig. 1.
Fig. 1. (a) Example DWFS caustic patterns from an emmetropic model eye (red) and 5D myopic eye (blue), and (b) corresponding spotfields from the SHWFS with the same refractive error and pseudocoloring as in (a). Note the periodic nature of the spotfield image, compared to the relatively random caustic pattern of the DWFS.
Fig. 2.
Fig. 2. (a) Diagram of SHWFS fundamental dynamic range and sensitivity constraints. At high wavefront tilts (α > αmax), spot displacement into an adjacent lenslet’s field of view causes origin ambiguity. At low wavefront tilts (α < αmin), spot displacement is less than a pixel. (b) A similar model is proposed for the holographic diffuser, where the effective diffuser focal length is the distance from diffuser surface to sharp caustic image formation (fD), and the effective diffuser pitch is the measured average distance between sharp caustic intensity peaks (ρD).
Fig. 3.
Fig. 3. Schematic of DWFS and SHWFS experimental setup. A collimated, slightly off-axis pencil beam was linearly polarized (P1), redirected with a beamsplitter (BS), and focused by the model eye lens (MEL) onto the model retina (MR). The resulting point-source illumination (occurring in the absence of a trial lens (TL)) is re-collimated by the MEL and relayed by a 1×, 4f telescopic system (RL1 and RL2) to the lenslet array of the SHWFS and the holographic diffuser of the DWFS simultaneously. A second crossed polarizer (P2) is used to mitigate back reflection. Various TLs are introduced, at a conjugate plane to the lenslet and diffuser, to characterize sensitivity and dynamic range.
Fig. 4.
Fig. 4. Outline of the DWFS algorithm. (a) A reference caustic from an emmetropic eye (red) was registered to a distorted caustic from an ametropic eye (blue). The resulting vector field displacement map (D⃗(x, y), green arrows) was scaled to produce the transverse gradient of the wavefront (∇δ⃗(x, y)). (b) 2D gradient integration provided a measurement of the wavefront (W(ρ, θ)). (c) The measured wavefront was decomposed into a Zernike basis and a refractive error was calculated.
Fig. 5.
Fig. 5. M measurements and dynamic range results for (a) laser diode, (b) laser diode with laser speckle reducer, and (c) LED illumination for the DWFS (red) and SHWFS (blue) for [−24D, +24D] trial lens tested. Dashed vertical lines represent the predicted dynamic range with αmax for the SHWFS (blue) and DWFS (red). * power-limited.
Fig. 6.
Fig. 6. Example caustic images (0D red, +16D blue) from the DWFS before registration (a), and after registration (b). Full field of view (left) and outlined regions of interest (right). The green arrow shows an example registered feature exceeding the ρD/2 cutoff criteria that limits a conventional SHWFS algorithm.
Fig. 7.
Fig. 7. J0 (top row) and J45 (bottom row) measurements for (a) laser diode, (b) laser diode with laser speckle reducer, and (c) LED illumination for the DWFS and SHWFS for [−4D, +4D] cylindrical trial lens tested at 0° and 45° axis.
Fig. 8.
Fig. 8. (a) Diffuser caustic from emmetropic model eye with LD+LSR illumination. Red dashed line represents the location of single plot profile taken across the diffuser caustic. (b) plot profile produced of red-dashed line in (a), with threshold intensity of 40 counts marked by the blue dashed line. 20 distinct peaks extend above this threshold over a distance of 6656μm.
Fig. 9.
Fig. 9. Schematic of an example myopic refractive error measurement in the SHWFS path. Note the thin lens approximation, similar right triangles defined by α, and Equations 12 allow a derivation of predicted dynamic range and sensitivity of the SHWFS and DWFS in terms of refractive error. The resulting inequality is shown below in Equation 10.
Fig. 10.
Fig. 10. Example spotfields (a)–(b) and caustics (c)–(d) demonstrating SHWFS and DWFS refractive error sensitivity and dynamic range predicted by Equation 10. For each image, red corresponds to an emmetropic eye, blue to myopic refractive error, and green to hyperopic refractive error. In each panel, a full frame 1024×1024 image is presented (left), with a 256×256 ROI outlined in yellow and magnified (right). (a) SHWFS spotfield image showing sensitivity to ±0.25D refractive error. Though spot intensity overlap occurs, centroid displacement is greater than Δx, visible by the color separation in the top right spot. (b) SHWFS spotfield image showing ±4.5D refractive error near the limit of the instrument’s dynamic range. Note spotfield displacement towards the periphery becomes (ρSH/2), visible where the green and blue spots overlap between two red spots. (c) DWFS caustics with ±0.50D refractive error, near the predicted sensitivity of the instrument. Color separation is just barely visible towards the periphery of the image. (d) DWFS caustics with ±12D refractive error, near the predicted dynamic range of the instrument. Note towards the edge of the pupil caustic displacement becomes nearly (ρD/2) visible where green and blue caustics overlap halfway between two red caustics.
Fig. 11.
Fig. 11. (a) Schematic of the effective focal length (EFL), back focal length (BFL), principal plane (PP) location, and conjugate plane for the 1×, 4f telescopic relay (CP) for PTL > 0D (myopic condition). (b) EFL, BFL, PP, and CP for PTL < 0D (hyperopic condition). Note that the distance between CP and PP is larger than in (a). (c) Calculation of changing EFL, BFL, and PP location for each of the [−24D, +24D] trial lens tested. Curves generated with Equation 11 thin lens, 0mm separation approximation are denoted with “d = 0” subscript. Curves generated from Gaussian reduction and correction for moving principal plane are denoted with “GR” subscript. (d) Simulated trial lens power (TLP) measurements with thin lens d = 0mm approximation (red dashed line) and with Gaussian reduction correction (blue solid line). M measurements from DWFS with LD+LSR illumination are plotted over these curves vs. TLPd=0 in blue x’s before correction, and vs. TLPGR in red o’s after correction.
Fig. 12.
Fig. 12. Registration results of multi-level Demon’s algorithm run on SHWFS spotfield images from [−10D, +10D]. Each image includes the 0D emmetropic spotfield (red), the Ptl > 0 trial lens spotfield after registration (blue), and the Ptl < 0 trial lens after registration (green). Note that after ±4D the registration algorithm begins to fail. This is approximately the same dynamic range found for the ρSH/2 criteria. This is in contrast to the DWFS caustic intensity pattern, which is able to register beyond ρD/2, as seen in Figure 6.

Tables (3)

Tables Icon

Table 1: Comparison of Attributes of SHWFS and DWFS

Tables Icon

Table 2. Spherical Error Measurement Results (* power-limited)

Tables Icon

Table 3. Measured J0 and J45 mean standard deviation (σ̄) and root-mean-square-error (RMSE) for the SHWFS and DWFS.

Equations (11)

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α max = ρ SH 2 f SH
α min = Δ x f SH
α max α min = ρ S H 2 Δ x
δ ( x , y ) D ( x , y ) f D
W ( ρ , θ ) = δ ( x , y ) d x d y
W ( ρ , θ ) = n = 1 N c i Z i ( ρ , θ )
θ A = 1 2 arctan c 4 c 6
ϕ 1 = [ 2 6 R max 2 ( c 4 sin ( 2 θ A ) + c 6 cos ( 2 θ A ) ) + 4 3 R max 2 c 5 ]
ϕ 2 = [ 2 6 R max 2 ( c 4 sin ( 2 θ A ) + c 6 cos ( 2 θ A ) ) 4 3 R max 2 c 5 ]
Δ x < f | s ( P t l ) f R L 2 f | * R S < ρ 2
P ME = P MEL + P TL

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