High Resolution Wavefront Sensing and Mirror Control for Vision Science by Quantitative Phase Imaging Alaster Meehan 1,2 , Phillip Bedggood 1 , Brendan Allman 2 , Keith Nugent 2 , Andrew Metha 1 Department of Optometry & Vision Sciences 1 , School of Physics 2 , the University of Melbourne, 3010, Australia Author e-mail address: a.meehan@pgrad.unimelb.edu.au Abstract: Quantitative Phase Imaging displays attractive features for ocular wavefront aberrometry. An adaptive-optics mirror control algorithm for ophthalmoscopy is demonstrated that takes advantage of its superior lateral resolution and similar accuracy compared to Hartmann- Shack systems. ©2009 Optical Society of America OCIS Codes: (100.5070) Phase retrieval, (110.1080) Active or adaptive optics 1. Introduction One of the most common wavefront sensors in the field of adaptive optics (AO) is the Hartmann-Shack (HS) wavefront sensor. The HS wavefront sensor is very reliable and accurate but is limited in resolution and range by the size and focal length of the lenslet array. It is sometimes desirable to have a higher resolution in a wavefront sensor particularly in the field of vision science where we may wish to study tear film effects, the precise effects of contact lenses and corneal damage that may occur during refractive surgery. High-resolution Adaptive Optics is also necessary to achieve enhanced imaging of the retina. Better retinal imaging can help us better understand the anatomy of a living eye and examine the effects of ageing and disease. In this paper we introduce the use of Quantitative Phase Imaging (QPI) as an alternative method for wavefront sensing. QPI can be used as a high resolution, fast and accurate wavefront sensor for adaptive optics in vision science. A new mirror control algorithm, useful for high-resolution wavefront sensors is also presented. 2. The QPI algorithm The QPI algorithm is based on a solution of the transport of intensity equation (TIE). The TIE explains the propagation of electromagnetic radiation and is primarily based on energy conservation. It is usefully expressed by a paraxial approximation that describes the energy flow in a particular direction represented by the z axis, x and y are coordinates perpendicular to energy flow. 2 π λ ∂ I ( x , y ) ∂ z =∇• I ( x , y ) ∇ φ ( x , y ) ( ) (1) Here,  is the wavelength of light, I(x,y) and φ (x,y) are the electromagnetic intensity and phase respectively, perpendicular to the direction of the energy flow, I(x,y) is the derivative of intensity, it is calculated by taking the difference of two images slightly out of focus I 1 –I 2 . A full derivation of Equation 1, the TIE, is given by Teague [1]. A Fourier based solution to the phase term (Equation 2) was developed and described by Paganin and Nugent [2]. φ = φ x + φ y φ x =− k F −1 k x k r 2 F 1 Ix , y ( ) F − 1 k x k r 2 F ∂ z Ix , y ( ) φ y =− k F −1 k y k r 2 F 1 Ix , y ( ) F − 1 k y k r 2 F ∂ z Ix , y ( )        (2) Here F -1 denotes the inverse Fourier transform, F denotes forward Fourier transform and k x and k y are the Fourier variables where k r 2 = k x 2 + k y 2 . This is a direct calculation of the phase of the wavefront, unlike other curvature sensors that use an iterative process to solve the wavefront [3], hence it is much faster to compute. The nature of the algorithm is also highly separable with only FFTs and image multiplications where each pixel is independent. The separable nature QPI lends itself to parallel computing. For example, computing QPI on a Graphics Processing Unit (GPU) achieves a ~10-fold increase in speed and gets 10 Mega Pixels per second output. a954_1.pdf JWB5.pdf © 2009 OSA/FiO/LS/AO/AIOM/COSI/LM/SRS 2009 JWB5.pdf