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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 23 — Nov. 12, 2007
  • pp: 15287–15292
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Measurement and compensation of optical aberrations using a single spatial light modulator

Justo Arines, Vicente Durán, Zbigniew Jaroszewicz, Jorge Ares, Enrique Tajahuerce, Paula Prado, Jesús Lancis, Salvador Bará, and Vicent Climent  »View Author Affiliations


Optics Express, Vol. 15, Issue 23, pp. 15287-15292 (2007)
http://dx.doi.org/10.1364/OE.15.015287


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Abstract

We describe a compact adaptive optical system using a spatial light modulator (SLM) as a single element to both measure and compensate optical aberrations. We used a low-cost, off-the-shelf twisted nematic liquid-crystal display (TNLCD) optimally configured to achieve maximum phase modulation with near constant transmittance. The TNLCD acts both as the microlens array of a Hartmann-Shack wavefront sensor and as the aberration compensation element. This adaptive setup is easy to implement and offers great versatility.

© 2007 Optical Society of America

1. Introduction

Adaptive systems have been successfully demonstrated in the last decades as efficient tools for compensating time-varying aberrations of optical fields [1

1. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, New York1998).

]. A conventional adaptive optical setup is composed of two basic subsystems, one of which measures the aberration and sends the appropriate control signals to the other one, which compensates it. The measurement subsystem consists on some kind of wavefront sensor, being the Hartmann-Shack the most widely used nowadays [2

2. R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

]. The compensation unit consists basically of a reconfigurable optical element, like a deformable mirror [3

3. E. Dalimier and C. Dainty, “Comparative analysis of deformable mirrors for ocular adaptive optics,” Opt. Express 13, 4275–4285 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-11-4275. [CrossRef] [PubMed]

] or a liquid crystal spatial light modulator [4

4. F. Vargas-Martin, P. M. Prieto, and P. Artal, “Correction of the aberrations in the human eye with a liquid crystal spatial light modulator: limits to performance,” J. Opt. Soc. Am. A 15, 2552–2562 (1998). [CrossRef]

].

Liquid crystal spatial light modulators (SLM) offer some interesting features, which make them an interesting option for several applications. Although few years ago the trend was to use specialized devices, which were designed and manufactured for adaptive optics applications [5

5. G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. 36, 1517–1524 (1997). [CrossRef] [PubMed]

, 6

6. P. M. Prieto, E. J. Fernández, S. Manzanera, and P. Artal, “Adaptive optics with a programmable phase modulator: applications in the human eye,” Opt. Express 12, 4059–4071 (2004). [CrossRef] [PubMed]

], there is presently a growing interest in using off-the-shelf, low cost SLM based on twisted nematic liquid crystal displays (TNLCD) like those commonly found in video projectors. The main disadvantages of these TNLCDs are their relatively small phase modulation depth and the need of using relatively narrowband polarized light, which are counterbalanced by their high spatial resolution, easy addressability, direct compatibility with usual hardware and software, low cost and wide availability. Besides, their performance is steadily improving, driven by the research oriented to the optoelectronics consumer market.

These TNLCDs have been used, in combination with polarizers and retarder waveplates, to build SLMs able to generate diffractive microlens arrays to implement Hartmann-Shack wavefront sensors [7

7. L. Seifert, J. Liesener, and H.J. Tiziani, “The adaptive Shack-Hartmann sensor,” Opt. Commun. 216, 313–319 (2003). [CrossRef]

,8

8. L. Zhao, N. Bai, X. Li, L.S. Ong, Z.P. Fang, and A.K. Asundi, “Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor,” Appl. Opt. 45, 90–94 (2006). [CrossRef] [PubMed]

] as well as to produce or compensate different kinds of optical aberrations [7

7. L. Seifert, J. Liesener, and H.J. Tiziani, “The adaptive Shack-Hartmann sensor,” Opt. Commun. 216, 313–319 (2003). [CrossRef]

,9

9. H.J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, “Application of SLMs for optical metrology,” in Spatial Light Modulators: Technology and Applications, Uzi Efron (Ed.), Proc. SPIE 4457, 72–81 (2001). [CrossRef]

,10

10. V. Durán, V. Climent, E. Tajahuerce, Z. Jaroszewicz, J. Arines, and S. Bará, “Efficient compensation of Zernike modes and eye aberration patterns using low-cost spatial light modulators,” J. Biomed. Opt. 12014037 (2007) [CrossRef] [PubMed]

]. In this work we combine these two possibilities to build a compact and versatile adaptive optics module using a single SLM acting both as the microlens array of a Hartmann-Shack wavefront sensor and as the aberration compensating element.

2. Basic layout of the adaptive setup

Fig. 1. Block diagram of the single SLM adaptive setup (see text for details).

3. Experimental results

In our experiments we used a TNLCD Sony Model LCX016AL, with an effective area of 26.6 × 21 mm2 and composed of 832 × 624 pixels (of effective size 26.7 × 21.3 μm2 each) arranged in a square array with center-to-center spacing of 32 μm. Optimum phase modulation was achieved with the help of two linear polarizers (P1, P2) and quarter-wave retarder plates (WP1, WP2) whose detailed configurations are described elsewhere [10

10. V. Durán, V. Climent, E. Tajahuerce, Z. Jaroszewicz, J. Arines, and S. Bará, “Efficient compensation of Zernike modes and eye aberration patterns using low-cost spatial light modulators,” J. Biomed. Opt. 12014037 (2007) [CrossRef] [PubMed]

, 12–13

12. V. Duran, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz: “Equivalent retarder-rotator approach to on-state twisted-nematic liquid crystal displays,” J. Appl. Phys. 99, 113101 (2006). [CrossRef]

] (see Fig.2). The TNLCD phase modulation response with a small residual intensity variation was achieved by using the calibration of a TNLCD based on the so-called equivalent retarder-rotator approach [12

12. V. Duran, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz: “Equivalent retarder-rotator approach to on-state twisted-nematic liquid crystal displays,” J. Appl. Phys. 99, 113101 (2006). [CrossRef]

]. The interpretation of a LC cell action as two successive rotations on the Poincaré sphere allowed to find a configuration for achieving phase-only modulation with a TNLCD based on the generation of equi-azimuth polarization states [13

13. V. Durán, J. Lancis, E. Tajahuerce, and M. Fernández-Alonso, “Phase-only modulation with a twisted nematic liquid crystal display by means of equi-azimuth polarization states,” Opt. Express 14, 5607–5616 (2006). [CrossRef] [PubMed]

].

Fig. 2. Experimental setup for achieving phase-only modulation of a TNLCD. P: polarizer; QWP: a quarter-wave plate. In the above diagram, the x-axis coincides with the input molecular director of the liquid crystal cell. P1 and P2 are, respectively, the orientation of the polarizer and the analyzer. L1 and L2 are the angles of the slow axis of the quarter-wave plates with respect to x-axis.

As light source we use a green LED (Luxeon Star LXHL-MM1D) with an emission spectrum centered in 530 nm with 35 nm bandwidth. Since the maximum depth modulation obtained with this device at 530 nm is slightly higher than 3π/2 rad, we used a four-level phase encoding scheme to display the wrapped phases corresponding to the microlens array and to the aberration compensating element. Full details of this procedure, as well as an analysis of its performance and limits can be found in Ref [10

10. V. Durán, V. Climent, E. Tajahuerce, Z. Jaroszewicz, J. Arines, and S. Bará, “Efficient compensation of Zernike modes and eye aberration patterns using low-cost spatial light modulators,” J. Biomed. Opt. 12014037 (2007) [CrossRef] [PubMed]

].

A demonstrative implementation of this setup is depicted in Fig. 3. Apart from the SLM (composed of P1-WP1-TNLCD-WP2-P2), three “4-f” optical systems are used, the first one (L1-L2,f'=160 mm) to project the input pupil on the TNLCD, the second one (L3-L4,f'=50 mm), in combination with a spatial filter (SF), used to remove the replicas of the wavefront produced by the diffraction grid formed by the square array of pixels of the TNLCD and a third one (L5-L6,f'=50 mm) to relay the image focal plane (IP') of L4 to the exit pupil. The first relay may be removed when the incoming aberrations are small enough as not to vary significantly by propagation across the space between the input pupil and the SLM [14

14. S. Bará, T. Mancebo, and E. Moreno-Barriuso, “Positioning tolerances for phase plates compensating aberrations of the human eye,” Appl. Opt. 39, 3413–3420 (2000). [CrossRef]

]. On the other hand, the last relay can be eliminated by shortening the system and allowing the spatial filtering module L3-SF-L4 to form its image IP' directly on the exit pupil. A lens L7 is used to image the focal plane of the microlens array encoded in the TNLCD onto a CCD camera in order to measure the aberrations in a classical Hartmann-Shack configuration.

Fig.3. Single SLM adaptive demonstration setup.

An additional optical path (not shown in Fig. 3) was used in our experiments in order to image onto separate areas of the CCD chip not only the focal plane of the microlens array, but also the image of the source (LED emitting area) given by the aberrated/compensated system, in order to get a simultaneous view of the system operation. The input aberrated beams, A, were produced with the help of photoresist phase plates encoding aberrations of shape and magnitude typical of human eyes [15

15. R. Navarro, E. Moreno-Barriuso, S. Bará, and T. Mancebo, “Phase-plates for wave-aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000). [CrossRef]

, 16

16. P. Rodríguez, R. Navarro, J. Arines, and S. Bará, “A New Calibration Set of Phase Plates for Ocular Aberrometers,” J. Refract. Surg. , 22, 275–284 (2006). [PubMed]

] and/or introducing increasing amounts of defocus.

Fig. 4. Grayscale representation of the four-level TNLCD patterns: (left) for generating a 9 × 9 diffractive microlens array; (right) for compensating the aberration produced by an artificial eye.

Typical four-level patterns sent to the TNLCD in the measurement and compensating steps are shown in Fig 4. Fig. 4 (left) corresponds to the pattern for generating a 9 × 9 diffractive microlens array with subpupil size 560 μm and focal length 4.2 cm (@ 530 nm) used in our experiments. Fig. 4 (right) corresponds to the pattern for compensating the aberration generated by an artificial eye with a phase plate representative of an eye aberration of average magnitude including high order Zernike terms up to 7th radial order (35 non trivial Zernike aberrations), with relatively strong astigmatic components and with partially corrected defocus.

Figure 5 shows the CCD images obtained at three consecutive slots of time in a typical demonstration run: Fig.5 (left), taken during the measurement step, shows at the left side the microlens array foci, and at the lower right the image of the LED source given by the system, strongly distorted due to the pass of the aberrated beam trough the microlens array; Fig.5 (center) shows an enlarged view of the original aberrated LED image, with the TNLCD in off-state. Finally, Fig. 5 (right) shows the corrected image, after the TNLCD was fed with the aberration (with opposite sign) computed after measurement. The collapsing of the aberrated PSF after compensation can be easily noticed. A low speed video of several aberration-compensation loops can be seen online clicking on Fig. 5 (left). To help visualize the compensation the loop was programmed to follow the steps displayed in the static images of this Figure, in such a way that the system first measures the aberration (LED image strongly distorted by the microlens array), then shows for a few seconds the aberrated LED image with the TNLCD in off state and finally the compensating phase is sent to the TNLCD (the PSF collapses and the LED image gets smaller).

Fig. 5. CCD images obtained at three consecutive time intervals in a typical demonstration run. Video file (4 MB) [Media 1]

Fig. 6. A real time video of the performance of the system when compensating continuously varying amounts of defocus. Video file (1.9 MB) [Media 2]

The timer indicates the elapsed time since the beginning of recording. Note in the video sequence that the compensation allows resolving the spatial structure of the LED emitting surface. The initially undistorted LED image is 7 pixels wide (FWHM) at the imaging camera (pixel size 6.4 μm). This FWHM quickly increases with defocus (e.g. it is 10 pixels for 0.1 D of defocus and 70 pìxels for 1.45 D of defocus). After compensation, the resulting measured width is 7 pixels again.

4 Additional remarks and conclusions

The proposed setup has some limitations common to most pixelated TNLCD-based SLM: (i) it requires the use of polarized light, so that for completely unpolarized input beams a 50% of the power is lost at the first polarizer P1; (ii) the light shall also be relatively narrowband, both for avoiding chromatic dispersion at the TNLCD cells and for allowing a proper functioning of the quarter-wave plates WP1, WP2, although, as it has been shown, it can cope well with a typical LED bandwidth and (iii) the spatial frequency content of the aberration to be efficiently compensated is limited by the Nyquist limit associated to the fundamental spatial frequency of the TNLCD pixel array (in order to allow a proper filtering of the unwanted diffraction orders, avoiding cross-talk). There are two additional power loss factors associated with some low-cost devices as that used in our experiments: the losses due to the relatively small fill factor of the TNLCD cells, and those due to the power going to diffraction orders other than that of interest, due to the use of a four-level phase encoding scheme. The spatial superposition of these diffraction orders with the compensated exit beam may be avoided by spatial filtering if a suitable carrier frequency is introduced on the SLM, at the expense of reducing the spatial bandwidth of the aberrations to be compensated for. The use of the four-level phase encoding is due to the 3π/2 phase modulation depth of our device and may be avoided if full 2π phase modulation cells are used.

Note that since the SLM measures the optical aberrations of the wavefront incident on it, the deleterious effects on the exit beam of the aberrations introduced by the SLM itself and all the optics located behind it must be carefully taken into account. In the experimental results shown in this paper these aberrations have not been compensated for. However this is not a fundamental limitation of this setup, since the static aberration introduced by all these elements may be measured once by conventional methods (e.g. interferometry or wavefront sensing), and the corresponding compensating phase may be encoded as a constant nulling term in the SLM to get rid of it (see e.g. Refs [7

7. L. Seifert, J. Liesener, and H.J. Tiziani, “The adaptive Shack-Hartmann sensor,” Opt. Commun. 216, 313–319 (2003). [CrossRef]

, 9

9. H.J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, “Application of SLMs for optical metrology,” in Spatial Light Modulators: Technology and Applications, Uzi Efron (Ed.), Proc. SPIE 4457, 72–81 (2001). [CrossRef]

, 10

10. V. Durán, V. Climent, E. Tajahuerce, Z. Jaroszewicz, J. Arines, and S. Bará, “Efficient compensation of Zernike modes and eye aberration patterns using low-cost spatial light modulators,” J. Biomed. Opt. 12014037 (2007) [CrossRef] [PubMed]

]).

No other fundamental factors limit the performance of this device, whose temporal bandwidth is determined in our case by our particular image acquisition and processing routines which can in principle be substantially improved. The main advantages of this setup are its great versatility, low cost, easy addressability and control and, last but not least, its seamless integration with the PC-based hardware and software commonly used in optoelectronics applications. Video projector TNLCDs are nothing else than computer screens in which different “images” are displayed to make the SLM act as a wavefront sampling device (a microlens array) or a wavefront corrector. No special drivers, external power supplies or specific programming are required.

Given the wavelength dependence and the power losses at the SLM, this adaptive setup is not, in its present form, particularly indicated for broad bandwidth or low irradiance applications such as incoherent imaging of faint astronomical sources through the turbulent atmosphere. Whether or not the light efficiency of this device is enough to apply it to near real time compensation of human eye aberrations is still to be determined. It is however quite well suited to be used as an active compensation unit in optical setups where the aberrations (even of highly complex shape and magnitude) are not very fast changing in time.

Acknowledgments

This work has been supported in part by the Spanish Ministerio de Educación y Ciencia, grants FIS2005-05020-C03-02, FIS2004-02404 and European Regional Development Fund, by the agreement between the Universitat Jaume I and the Fundació Caixa Castelló (Bancaixa), grant P1-1B2006-29 and by the Polish Ministerstwo Nauki i Informatyzacji under Contract Number 4 T07D 003 29 1691/T07/2005/29.

References and links

1.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, New York1998).

2.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

3.

E. Dalimier and C. Dainty, “Comparative analysis of deformable mirrors for ocular adaptive optics,” Opt. Express 13, 4275–4285 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-11-4275. [CrossRef] [PubMed]

4.

F. Vargas-Martin, P. M. Prieto, and P. Artal, “Correction of the aberrations in the human eye with a liquid crystal spatial light modulator: limits to performance,” J. Opt. Soc. Am. A 15, 2552–2562 (1998). [CrossRef]

5.

G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. 36, 1517–1524 (1997). [CrossRef] [PubMed]

6.

P. M. Prieto, E. J. Fernández, S. Manzanera, and P. Artal, “Adaptive optics with a programmable phase modulator: applications in the human eye,” Opt. Express 12, 4059–4071 (2004). [CrossRef] [PubMed]

7.

L. Seifert, J. Liesener, and H.J. Tiziani, “The adaptive Shack-Hartmann sensor,” Opt. Commun. 216, 313–319 (2003). [CrossRef]

8.

L. Zhao, N. Bai, X. Li, L.S. Ong, Z.P. Fang, and A.K. Asundi, “Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor,” Appl. Opt. 45, 90–94 (2006). [CrossRef] [PubMed]

9.

H.J. Tiziani, T. Haist, J. Liesener, M. Reicherter, and L. Seifert, “Application of SLMs for optical metrology,” in Spatial Light Modulators: Technology and Applications, Uzi Efron (Ed.), Proc. SPIE 4457, 72–81 (2001). [CrossRef]

10.

V. Durán, V. Climent, E. Tajahuerce, Z. Jaroszewicz, J. Arines, and S. Bará, “Efficient compensation of Zernike modes and eye aberration patterns using low-cost spatial light modulators,” J. Biomed. Opt. 12014037 (2007) [CrossRef] [PubMed]

11.

W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980). [CrossRef]

12.

V. Duran, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz: “Equivalent retarder-rotator approach to on-state twisted-nematic liquid crystal displays,” J. Appl. Phys. 99, 113101 (2006). [CrossRef]

13.

V. Durán, J. Lancis, E. Tajahuerce, and M. Fernández-Alonso, “Phase-only modulation with a twisted nematic liquid crystal display by means of equi-azimuth polarization states,” Opt. Express 14, 5607–5616 (2006). [CrossRef] [PubMed]

14.

S. Bará, T. Mancebo, and E. Moreno-Barriuso, “Positioning tolerances for phase plates compensating aberrations of the human eye,” Appl. Opt. 39, 3413–3420 (2000). [CrossRef]

15.

R. Navarro, E. Moreno-Barriuso, S. Bará, and T. Mancebo, “Phase-plates for wave-aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000). [CrossRef]

16.

P. Rodríguez, R. Navarro, J. Arines, and S. Bará, “A New Calibration Set of Phase Plates for Ocular Aberrometers,” J. Refract. Surg. , 22, 275–284 (2006). [PubMed]

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(220.1000) Optical design and fabrication : Aberration compensation
(230.3720) Optical devices : Liquid-crystal devices
(230.6120) Optical devices : Spatial light modulators

ToC Category:
Adaptive Optics

History
Original Manuscript: July 13, 2007
Revised Manuscript: September 17, 2007
Manuscript Accepted: September 24, 2007
Published: November 2, 2007

Citation
Justo Arines, Vicente Durán, Zbigniew Jaroszewicz, Jorge Ares, Enrique Tajahuerce, Paula Prado, Jesús Lancis, Salvador Bará, and Vicent Climent, "Measurement and compensation of optical aberrations using a single spatial light modulator," Opt. Express 15, 15287-15292 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-23-15287


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References

  1. J. W.  Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, New York 1998).
  2. R. V. Shack and B. C. Platt, "Production and use of a lenticular Hartmann screen," J. Opt. Soc. Am. 61, 656 (1971).
  3. E. Dalimier and C. Dainty, "Comparative analysis of deformable mirrors for ocular adaptive optics," Opt. Express 13, 4275-4285 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-11-4275>. [CrossRef] [PubMed]
  4. F. Vargas-Martin, P. M. Prieto and P. Artal, "Correction of the aberrations in the human eye with a liquid crystal spatial light modulator: limits to performance," J. Opt. Soc. Am. A 15, 2552-2562 (1998). [CrossRef]
  5. G. D. Love, "Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator," Appl. Opt. 36, 1517-1524 (1997). [CrossRef] [PubMed]
  6. P. M. Prieto, E. J. Fernández, S. Manzanera and P. Artal, "Adaptive optics with a programmable phase modulator: applications in the human eye," Opt. Express 12, 4059-4071 (2004). [CrossRef] [PubMed]
  7. L. Seifert, J. Liesener and H.J. Tiziani, "The adaptive Shack-Hartmann sensor," Opt. Commun. 216, 313-319 (2003). [CrossRef]
  8. L. Zhao, N. Bai, X. Li, L. S. Ong, Z. P. Fang and A. K. Asundi, "Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor," Appl. Opt. 45, 90-94 (2006). [CrossRef] [PubMed]
  9. H. J. Tiziani, T. Haist, J. Liesener, M. Reicherter and L. Seifert, "Application of SLMs for optical metrology," Proc. SPIE 4457, 72-81 (2001). [CrossRef]
  10. V. Durán, V. Climent, E. Tajahuerce, Z. Jaroszewicz, J. Arines and S. Bará, "Efficient compensation of Zernike modes and eye aberration patterns using low-cost spatial light modulators," J. Biomed. Opt. 12, 014037 (2007) [CrossRef] [PubMed]
  11. W. H. Southwell, "Wave-front estimation from wave-front slope measurements," J. Opt. Soc. Am. 70, 998-1006 (1980). [CrossRef]
  12. V. Duran, J. Lancis, E. Tajahuerce, and Z. Jaroszewicz: "Equivalent retarder-rotator approach to on-state twisted-nematic liquid crystal displays," J. Appl. Phys. 99, 113101 (2006). [CrossRef]
  13. V. Durán, J. Lancis, E. Tajahuerce, and M. Fernández-Alonso, "Phase-only modulation with a twisted nematic liquid crystal display by means of equi-azimuth polarization states," Opt. Express 14, 5607-5616 (2006). [CrossRef] [PubMed]
  14. S. Bará, T. Mancebo and E. Moreno-Barriuso, "Positioning tolerances for phase plates compensating aberrations of the human eye," Appl. Opt. 39, 3413-3420 (2000). [CrossRef]
  15. R. Navarro, E. Moreno-Barriuso, S. Bará, and T. Mancebo, "Phase-plates for wave-aberration compensation in the human eye," Opt. Lett. 25, 236 - 238 (2000). [CrossRef]
  16. P. Rodríguez, R. Navarro, J. Arines and S. Bará, "A New Calibration Set of Phase Plates for Ocular Aberrometers," J. Refract. Surg.  22, 275-284 (2006). [PubMed]

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