1
|
Haber A, Bifano T. Dual-update data-driven control of deformable mirrors using Walsh basis functions. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2022; 39:459-469. [PMID: 35297430 DOI: 10.1364/josaa.447879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Accepted: 01/29/2022] [Indexed: 06/14/2023]
Abstract
We develop a novel data-driven method for deformable mirror (DM) control. The developed method updates both the DM model and DM control actions that produce desired mirror surface shapes. The novel method explicitly takes into account actuator constraints and couples a feedback-control algorithm with an algorithm for recursive estimation of DM influence function models. We also explore the possibility of using Walsh basis functions for DM control. By expressing the desired and observed mirror surface shapes as sums of Walsh pattern matrices, we formulate the control problem in the 2D Walsh basis domain. We thoroughly experimentally verify the developed approach on a 140-actuator MEMS DM, developed by Boston Micromachines. Our results show that the novel method produces the root-mean-square surface error in the 14-40 nanometer range. These results can additionally be improved by tuning the control and estimation parameters. The developed approach is also applicable to other DM types such as segmented DMs.
Collapse
|
2
|
Haber A, Bifano T. General approach to precise deformable mirror control. OPTICS EXPRESS 2021; 29:33741-33759. [PMID: 34809180 DOI: 10.1364/oe.439306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Accepted: 09/23/2021] [Indexed: 06/13/2023]
Abstract
We develop a simple and effective control method for accurate control of deformable mirrors (DMs). For a desired DM surface profile and using batches of observed surface profile data, the proposed method adaptively determines both a DM model (influence matrix) and control actions that produce the desired surface profile with good accuracy. In the first iteration, the developed method estimates a DM influence matrix by solving a multivariable least-squares problem. This matrix is then used to compute the control actions by solving a constrained least-squares problem. Then, the computed actions are randomly perturbed and applied to the DM to generate a new batch of surface profile data. The new data batch is used to estimate a new influence matrix that is then used to re-compute control actions. This procedure is repeated until convergence is achieved. The method is experimentally tested on a Boston Micromachines DM with 140 micro-electronic-mechanical-system actuators. Our experimental results show that the developed control approach can achieve accurate correction despite significant DM nonlinearities. Using only a few control iterations, the developed method is able to produce a surface profile root-mean-square error that varies from 5 - 30 [nm] for most of the tested Zernike wave-front modes without using direct feedback control. These results can additionally be improved by using larger data batches and more iterations or by combining the developed approach with feedback control. Finally, as we experimentally demonstrate, the developed method can be used to estimate a DM model that can effectively be used for a single-step open-loop DM control.
Collapse
|
3
|
Zhang L, Li C, Huang X, Zhang Y, Zhou S, Li J, Yu B. Compact adaptive interferometer for unknown freeform surfaces with large departure. OPTICS EXPRESS 2020; 28:1897-1913. [PMID: 32121892 DOI: 10.1364/oe.380889] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Accepted: 01/02/2020] [Indexed: 06/10/2023]
Abstract
The newest experimental validation report of the coverage for the rotationally non-symmetric departure of a freeform surface in adaptive interferometry is about 20 µm. A compact adaptive interferometer is introduced to test unknown freeform surfaces with larger departure. The cascaded DMs (woofer and tweeter) can effectively double the measurable rotationally non-symmetric departure, to ∼80 µm using current DM technology. With a constrained decoupling control algorithm, the woofer and tweeter can averagely share the aberrations without coupling. DM surface monitoring is addressed by a time-division-monitoring (TDM) technique, which avoids separate monitoring devices and configurations and thus makes a compact configuration. Measurements of two different surfaces are presented: a nearly flat freeform with ∼40 um departure, and an off-axis paraboloid with ∼50 um of asymmetric departure.
Collapse
|
4
|
Cheng T, Liu W, Yang K, He X, Yang P, Xu B. Testing for a slope-based decoupling algorithm in a woofer-tweeter adaptive optics system. APPLIED OPTICS 2018; 57:3357-3364. [PMID: 29726501 DOI: 10.1364/ao.57.003357] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2017] [Accepted: 03/23/2018] [Indexed: 06/08/2023]
Abstract
It is well known that using two or more deformable mirrors (DMs) can improve the compensation ability of an adaptive optics (AO) system. However, to keep the stability of an AO system, the correlation between the multiple DMs must be suppressed during the correction. In this paper, we proposed a slope-based decoupling algorithm to simultaneous control the multiple DMs. In order to examine the validity and practicality of this algorithm, a typical woofer-tweeter (W-T) AO system was set up. For the W-T system, a theory model was simulated and the results indicated in theory that the algorithm we presented can selectively make woofer and tweeter correct different spatial frequency aberration and suppress the cross coupling between the dual DMs. At the same time, the experimental results for the W-T AO system were consistent with the results of the simulation, which demonstrated in practice that this algorithm is practical for the AO system with dual DMs.
Collapse
|
5
|
Marín-Franch I, Del Águila-Carrasco AJ, Levecq X, López-Gil N. Drifts in real-time partial wavefront correction and how to avoid them. APPLIED OPTICS 2017; 56:3989-3994. [PMID: 29047526 DOI: 10.1364/ao.56.003989] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In visual experiments that require real-time partial correction of wavefront aberrations, small errors occur that accumulate over time and lead to drifts in Zernike coefficients of the uncorrected aberrations. A simple algorithm that does not require the inclusion of an additional optical path to obtain independent measurements of the eye's aberrations is described here, and its effectiveness in preventing these drifts is demonstrated.
Collapse
|
6
|
Yu Y, Zhang T, Meadway A, Wang X, Zhang Y. High-speed adaptive optics for imaging of the living human eye. OPTICS EXPRESS 2015; 23:23035-52. [PMID: 26368408 PMCID: PMC4646518 DOI: 10.1364/oe.23.023035] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2015] [Revised: 08/10/2015] [Accepted: 08/10/2015] [Indexed: 05/18/2023]
Abstract
The discovery of high frequency temporal fluctuation of human ocular wave aberration dictates the necessity of high speed adaptive optics (AO) correction for high resolution retinal imaging. We present a high speed AO system for an experimental adaptive optics scanning laser ophthalmoscope (AOSLO). We developed a custom high speed Shack-Hartmann wavefront sensor and maximized the wavefront detection speed based upon a trade-off among the wavefront spatial sampling density, the dynamic range, and the measurement sensitivity. We examined the temporal dynamic property of the ocular wavefront under the AOSLO imaging condition and improved the dual-thread AO control strategy. The high speed AO can be operated with a closed-loop frequency up to 110 Hz. Experiment results demonstrated that the high speed AO system can provide improved compensation for the wave aberration up to 30 Hz in the living human eye.
Collapse
Affiliation(s)
- Yongxin Yu
- Department of Ophthalmology, University of Alabama at Birmingham, 1670 University Boulevard, Birmingham, AL 35294, USA
- School of Computer Science and Technology, Tianjin University, Tianjin 300072, China
| | - Tianjiao Zhang
- Department of Biomedical Engineering, University of Alabama at Birmingham, 1825 University Boulevard, Birmingham, AL 35294, USA
| | - Alexander Meadway
- Department of Ophthalmology, University of Alabama at Birmingham, 1670 University Boulevard, Birmingham, AL 35294, USA
| | - Xiaolin Wang
- Department of Ophthalmology, University of Alabama at Birmingham, 1670 University Boulevard, Birmingham, AL 35294, USA
| | - Yuhua Zhang
- Department of Ophthalmology, University of Alabama at Birmingham, 1670 University Boulevard, Birmingham, AL 35294, USA
- Department of Biomedical Engineering, University of Alabama at Birmingham, 1825 University Boulevard, Birmingham, AL 35294, USA
| |
Collapse
|
7
|
Huang L, Ma X, Bian Q, Li T, Zhou C, Gong M. High-precision system identification method for a deformable mirror in wavefront control. APPLIED OPTICS 2015; 54:4313-4317. [PMID: 25967482 DOI: 10.1364/ao.54.004313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2015] [Accepted: 04/14/2015] [Indexed: 06/04/2023]
Abstract
Based on a mathematic model, the relation between the accuracy of the influence matrix and the performance of the wavefront correction is established. Based on the least squares method, a two-step system identification is proposed to improve the accuracy of the influence matrix, where the measurement noise can be suppressed and the nonlinearity of the deformable mirror can be compensated. The validity of the two-step system identification method is tested in the experiment, where improvements in wavefront correction precision as well as closed-loop control efficiency were observed.
Collapse
|
8
|
Guo Y, Rao C, Bao H, Zhang A, Zhang X, Wei K. Multichannel-Hadamard calibration of high-order adaptive optics systems. OPTICS EXPRESS 2014; 22:13792-13803. [PMID: 24921571 DOI: 10.1364/oe.22.013792] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
we present a novel technique of calibrating the interaction matrix for high-order adaptive optics systems, called the multichannel-Hadamard method. In this method, the deformable mirror actuators are firstly divided into a series of channels according to their coupling relationship, and then the voltage-oriented Hadamard method is applied to these channels. Taking the 595-element adaptive optics system as an example, the procedure is described in detail. The optimal channel dividing is discussed and tested by numerical simulation. The proposed method is also compared with the voltage-oriented Hadamard only method and the multichannel only method by experiments. Results show that the multichannel-Hadamard method can produce significant improvement on interaction matrix measurement.
Collapse
|
9
|
Yu Y, Zhang Y. Dual-thread parallel control strategy for ophthalmic adaptive optics. CHINESE OPTICS LETTERS : COL 2014; 12:121202. [PMID: 25866498 PMCID: PMC4389685 DOI: 10.3788/col201412.121202] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
To improve ophthalmic adaptive optics speed and compensate for ocular wavefront aberration of high temporal frequency, the adaptive optics wavefront correction has been implemented with a control scheme including 2 parallel threads; one is dedicated to wavefront detection and the other conducts wavefront reconstruction and compensation. With a custom Shack-Hartmann wavefront sensor that measures the ocular wave aberration with 193 subapertures across the pupil, adaptive optics has achieved a closed loop updating frequency up to 110 Hz, and demonstrated robust compensation for ocular wave aberration up to 50 Hz in an adaptive optics scanning laser ophthalmoscope.
Collapse
Affiliation(s)
- Yongxin Yu
- School of Computer Science and Technology, Tianjin University, Tianjin 300072, China
- Department of Ophthalmology, University of Alabama at Birmingham, 1670 University Boulevard, Birmingham, AL 35294, USA
| | - Yuhua Zhang
- Department of Ophthalmology, University of Alabama at Birmingham, 1670 University Boulevard, Birmingham, AL 35294, USA
| |
Collapse
|
10
|
Liu W, Dong L, Yang P, Lei X, Yan H, Xu B. A Zernike mode decomposition decoupling control algorithm for dual deformable mirrors adaptive optics system. OPTICS EXPRESS 2013; 21:23885-23895. [PMID: 24104299 DOI: 10.1364/oe.21.023885] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
A simple but effective decoupling control algorithm based on Zernike mode decomposition for adaptive optics systems with dual deformable mirrors is proposed. One of the two deformable mirrors is characterized with a large stroke (woofer) and the other with high spatial resolutions (tweeter). The algorithm works as follows: wavefront gradient vector is decoupled using the Zernike modes at first, and then the control vector for the woofer is generated with low order Zernike coefficients to eliminate high order modes. At the same time the control vector for the tweeter is reset by a constraint matrix in order to avoid coupling error accumulation. Simulation indicates the algorithm could get better performance compared with traditional Zernike mode decomposition control algorithms. Experiments demonstrate that this algorithm can effectively compensate for phase distortions and significantly suppress the coupling between the woofer and tweeter.
Collapse
|
11
|
Zou W, Burns SA. Testing of Lagrange multiplier damped least-squares control algorithm for woofer-tweeter adaptive optics. APPLIED OPTICS 2012; 51:1198-208. [PMID: 22441462 PMCID: PMC3407539 DOI: 10.1364/ao.51.001198] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2011] [Accepted: 12/13/2011] [Indexed: 05/24/2023]
Abstract
A Lagrange multiplier-based damped least-squares control algorithm for woofer-tweeter (W-T) dual deformable-mirror (DM) adaptive optics (AO) is tested with a breadboard system. We show that the algorithm can complementarily command the two DMs to correct wavefront aberrations within a single optimization process: the woofer DM correcting the high-stroke, low-order aberrations, and the tweeter DM correcting the low-stroke, high-order aberrations. The optimal damping factor for a DM is found to be the median of the eigenvalue spectrum of the influence matrix of that DM. Wavefront control accuracy is maximized with the optimized control parameters. For the breadboard system, the residual wavefront error can be controlled to the precision of 0.03 μm in root mean square. The W-T dual-DM AO has applications in both ophthalmology and astronomy.
Collapse
Affiliation(s)
- Weiyao Zou
- School of Optometry, Indiana University, 800 East Atwater Avenue, Bloomington, Indiana 47405, USA.
| | | |
Collapse
|
12
|
Huang H, Inoue T, Tanaka H. Stabilized high-accuracy correction of ocular aberrations with liquid crystal on silicon spatial light modulator in adaptive optics retinal imaging system. OPTICS EXPRESS 2011; 19:15026-15040. [PMID: 21934864 DOI: 10.1364/oe.19.015026] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We studied the long-term optical performance of an adaptive optics scanning laser ophthalmoscope that uses a liquid crystal on silicon spatial light modulator to correct ocular aberrations. The system achieved good compensation of aberrations while acquiring images of fine retinal structures, excepting during sudden eye movements. The residual wavefront aberrations collected over several minutes in several situations were statistically analyzed. The mean values of the root-mean-square residual wavefront errors were 23-30 nm, and for around 91-94% of the effective time the errors were below the Marechal criterion for diffraction limited imaging. The ability to axially shift the imaging plane to different retinal depths was also demonstrated.
Collapse
Affiliation(s)
- Hongxin Huang
- Central Research Laboratory, Hamamatsu Photonics KK, 5000 Hirakuchi, Hamakita-Ku, Hamamatsu-City, Shizuoka 434-8601, Japan.
| | | | | |
Collapse
|
13
|
Zou W, Qi X, Burns SA. Woofer-tweeter adaptive optics scanning laser ophthalmoscopic imaging based on Lagrange-multiplier damped least-squares algorithm. BIOMEDICAL OPTICS EXPRESS 2011; 2:1986-2004. [PMID: 21750774 PMCID: PMC3130583 DOI: 10.1364/boe.2.001986] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2011] [Revised: 06/07/2011] [Accepted: 06/10/2011] [Indexed: 05/22/2023]
Abstract
We implemented a Lagrange-multiplier (LM)-based damped least-squares (DLS) control algorithm in a woofer-tweeter dual deformable-mirror (DM) adaptive optics scanning laser ophthalmoscope (AOSLO). The algorithm uses data from a single Shack-Hartmann wavefront sensor to simultaneously correct large-amplitude low-order aberrations by a woofer DM and small-amplitude higher-order aberrations by a tweeter DM. We measured the in vivo performance of high resolution retinal imaging with the dual DM AOSLO. We compared the simultaneous LM-based DLS dual DM controller with both single DM controller, and a successive dual DM controller. We evaluated performance using both wavefront (RMS) and image quality metrics including brightness and power spectrum. The simultaneous LM-based dual DM AO can consistently provide near diffraction-limited in vivo routine imaging of human retina.
Collapse
|
14
|
Godara P, Dubis AM, Roorda A, Duncan JL, Carroll J. Adaptive optics retinal imaging: emerging clinical applications. Optom Vis Sci 2010; 87:930-41. [PMID: 21057346 PMCID: PMC3017557 DOI: 10.1097/opx.0b013e3181ff9a8b] [Citation(s) in RCA: 123] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022] Open
Abstract
The human retina is a uniquely accessible tissue. Tools like scanning laser ophthalmoscopy and spectral domain-optical coherence tomography provide clinicians with remarkably clear pictures of the living retina. Although the anterior optics of the eye permit such non-invasive visualization of the retina and associated pathology, the same optics induce significant aberrations that obviate cellular-resolution imaging in most cases. Adaptive optics (AO) imaging systems use active optical elements to compensate for aberrations in the optical path between the object and the camera. When applied to the human eye, AO allows direct visualization of individual rod and cone photoreceptor cells, retinal pigment epithelium cells, and white blood cells. AO imaging has changed the way vision scientists and ophthalmologists see the retina, helping to clarify our understanding of retinal structure, function, and the etiology of various retinal pathologies. Here, we review some of the advances that were made possible with AO imaging of the human retina and discuss applications and future prospects for clinical imaging.
Collapse
Affiliation(s)
- Pooja Godara
- Department of Ophthalmology, Medical College of Wisconsin, Milwaukee, Wisconsin 53226, USA
| | | | | | | | | |
Collapse
|
15
|
Li C, Sredar N, Ivers KM, Queener H, Porter J. A correction algorithm to simultaneously control dual deformable mirrors in a woofer-tweeter adaptive optics system. OPTICS EXPRESS 2010; 18:16671-84. [PMID: 20721058 PMCID: PMC2929183 DOI: 10.1364/oe.18.016671] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
We present a direct slope-based correction algorithm to simultaneously control two deformable mirrors (DMs) in a woofer-tweeter adaptive optics system. A global response matrix was derived from the response matrices of each deformable mirror and the voltages for both deformable mirrors were calculated simultaneously. This control algorithm was tested and compared with a 2-step sequential control method in five normal human eyes using an adaptive optics scanning laser ophthalmoscope. The mean residual total root-mean-square (RMS) wavefront errors across subjects after adaptive optics (AO) correction were 0.128 +/- 0.025 microm and 0.107 +/- 0.033 microm for simultaneous and 2-step control, respectively (7.75-mm pupil). The mean intensity of reflectance images acquired after AO convergence was slightly higher for 2-step control. Radially-averaged power spectra calculated from registered reflectance images were nearly identical for all subjects using simultaneous or 2-step control. The correction performance of our new simultaneous dual DM control algorithm is comparable to 2-step control, but is more efficient. This method can be applied to any woofer-tweeter AO system.
Collapse
Affiliation(s)
- Chaohong Li
- College of Optometry, University of Houston, 505 J. Davis Armistead Bldg., Houston, TX 77204-2020,
USA
| | - Nripun Sredar
- College of Optometry, University of Houston, 505 J. Davis Armistead Bldg., Houston, TX 77204-2020,
USA
| | - Kevin M. Ivers
- College of Optometry, University of Houston, 505 J. Davis Armistead Bldg., Houston, TX 77204-2020,
USA
| | - Hope Queener
- College of Optometry, University of Houston, 505 J. Davis Armistead Bldg., Houston, TX 77204-2020,
USA
| | - Jason Porter
- College of Optometry, University of Houston, 505 J. Davis Armistead Bldg., Houston, TX 77204-2020,
USA
| |
Collapse
|