4. Wavefront Sensing Technology
Several wavefront sensing techniques have been developed for the measurement of the wavefront error in human eyes. Most wavefront sensors are based on the same principle, which is an indirect measurement of the first or second derivatives of the wavefront at the location of the pupil plane of the eye and the reconstruction of the complete wavefront by integrating these derivatives. In general, the apparatus directs a small beam of light into the eye which then backscatters off the retina. The scattered light leaving the eye gets aberrated by the eye's optics before being recorded by the imaging components of the wavefront sensor.
The Shack-Hartmann (S-H) type wavefront sensor is the most common method for measuring ocular aberrations. The device was introduced in clinical ophthalmology in 1994 [26, 27] and uses an array of micro-lenslets each of which observes the out-going beam at a different pupil location. The resulting light, aberrated by the eye's optics, is focused as an array of spots onto a detector. The best estimate of each spot's position and how far it deviates from a reference is calculated. The result is proportional to the average wavefront slope at that particular location of the pupil. Detailed information on the principle of S-H wavefront sensing can be found in previous work [25]. Limitations of the method include the quantity of light needed, the dynamic range and the fact that analysis of data from a S-H sensor does not consider the quality of the individual spots formed by the lenslet array [25]. However, experience has shown that the quality of spot images can vary greatly over the pupil of a human eye. If the wavefront shape within a single lenslet varies significantly, the spot pattern formed by that lenslet will be blurred making it more difficult to estimate its location. In the context of wavefront sensing, the term dynamic range represents the maximum wavefront slope that can be reliably measured. The dynamic range of the S-H sensor is strictly related to the optical parameters of the S-H microlenses: the lenslet spacing (or number of lenslet across the pupil) and the focal length of the lenslet array. Several methods have been used to increase the dynamic range of the S-H sensor, including a precompensation of LOA, the use of a larger lenslet diameter and/or a shorter focal length lenslet, restriction of the illuminating beam diameter, the magnification of the pupil at the lenslet array etc.[25, 28–32].
Due to the increasing interest and application of wavefront sensing techniques in the ophthalmic community in recent years, innovative methodologies have been designed and developed. Curvature sensing, pyramid sensing and interferometry are the most promising emerging wavefront sensing techniques.
Curvature sensing technology is based on phase-diversity. It depends on comparisons between phases in adjacent areas in the image and objective plane of an optical system [33–37]. Phase diversity is normally implemented by recording two images at different focal planes, and then reconstructing the wavefront from these images. Aberrations in the wavefront in the measurement plane will alter the local intensities of the wavefront as it propagates. A convex distortion will cause the wavefront to converge and hence become more intense, the contrary will be the case for a concave distortion. The change in intensity is a measure of the local wavefront curvature and may be used to reconstruct the wavefront. The Curvature Sensor (C-S) was originally developed for astronomical observation based on the technique developed by Roddier in 1988 [38]. His original idea was to directly couple a curvature sensor element and a bimorph deformable mirror, without the need for intermediate calculations, in an AO astronomical telescope. Experimental work by Diaz-Douton et al.[39] has demonstrated the feasibility of a curvature sensor for ocular wavefront measurement. The advantages of the C-S are its relatively high dynamic range and low cost, while the disadvantages are related to the prolonged time of computing and the fact that a large defocus is needed to measure the wavefront with higher resolution, thus reducing the sensitivity of the sensor. This means that the C-S might not be as accurate as expected for measuring HOA. On the other hand, this problem could be overcome by designing a C-S in which the defocusing distance can be adjusted to the individual eye [25].
The pyramid sensor (P-S) was developed by Ragazzoni and implemented for the first time in an astronomical AO system [40, 41]. In this system, a transparent pyramid splits the stellar image into four parts. Each beam forms an image of the telescope pupil on the same detector. A four-faceted refractive pyramid is placed in the optical path with its apex aligned to the optical axis facing the incoming beam. The wavefront gradients along two orthogonal directions are retrieved from the intensity distribution among the four pupil images resulting from this operation. The first application of a P-S sensor in ophthalmology was demonstrated by Iglesias et al.[42] in 2002, who used this method to measure the WA of artificial and normal eyes. They also pointed out the necessity to deal with spurious reflections from the anterior cornea. Chamot et al.[43] developed an ophthalmic AO system with a P-S in the measurement arm of the device and a piezoelectric deformable mirror (DM) as wavefront corrector element. The DM was optically conjugated to a steering mirror positioned in the wavefront sensor arm immediately before the tip of the diffractive pyramid element; this modulates the position of the image on the pyramid tip in a circular manner and facilitates quantitative measurement of the wavefront slopes. Tests were performed in artificial and human eyes achieving results similar to those obtained by other AO systems implemented with a S-H sensor, further demonstrating the feasibility and accuracy of the P-S sensing technique in an AO system for ophthalmic applications. One of the main advantages of a P-S is the easy adaptability of the system to the variations in the range of the aberrations one can expect in the human eye optics. The dynamic range of the sensor can be therefore quickly modified. Moreover, at small modulation amplitudes the sensitivity of a pyramidal sensor can be higher than that of a S-H sensor.
A variety of interferometry techniques have been suggested for ocular wavefront sensing, including shearing interferometry [44–49] and Talbot interferometry [50–52]. The common advantages of all the interferometric techniques is their relatively simple and inexpensive design if compared to other opto-electronic systems, as well as their accuracy, high spatial resolution and large dynamic range. The disadvantages are the sensitivity to vibration, changes in polarization of the beam coming back out of the eye and the complex reconstruction of the phase error. All these factors limit widespread application of this technology to human eyes. Among the interferometric techniques, Talbot interferometry has gained the most interest for application in vision science [25]. It is constructed with two gratings in which moiré fringes are generated by superimposing the Fourier image of the first grating on the second. The two gratings should have the same period. If the phase object is placed in front of the first grating, the light deflected by the object yields the shifted Fourier images and the resultant moiré fringes show the deflection mapping [50]. On the other hand, only one periodic grating can be used for phase distortion analysis, by exploiting the Talbot effect or self-imaging phenomenon [52]. The Talbot image can be directly detected by a detector placed at the Talbot distance from the periodic pattern, as described in previous work [25]. Distortion of the fringe pattern reflects the local tilt of the wavefront. This pattern can be observed only at a very short distance from the grating due to diffraction and the pattern disappears as distance increases. Diffraction patterns can be observed again at specific periodic distances from the grating. These are called Talbot images. Sekine et al.[53] used a two-dimensional grating for sensing the optical wavefront with the CCD placed in the plane of the Talbot image of the first order to maximize the contrast of the grating image. They obtained Talbot images from both artificial and human eyes and were able to successfully reconstruct wavefront shapes, with no discernible differences in comparison with those obtained by a S-H sensor. Warden et al.[54] demonstrated accurate results using a Talbot wavefront sensor which has recently become available commercially. A series of measurements was taken in model eyes demonstrating the high accuracy of the Talbot sensor in comparison with two commercially available S-H sensors, especially for HOA.