Optics Observations Pinholes, apertures and diffraction Lenses, lensmaker and depth of focus Two-dimensions and asymmetries Chromatic aberration of the human eye Adaptive optics, H-S Encoding

Pinhole optics

Lens Design: Snell’s Law

Lensmaker’s Equation

Optical power and object distance

Diffraction Limits The Sharpness Of Image With A Small Pinhole (From Jenkins and White, I think) Diffraction Limits The Sharpness Of Image With A Small Pinhole Aperture

The Diffraction Pattern Of A Disk Has A Formula Based on Bessel Functions That Can Be Calculated From First Principles Airy

Some Animals Have Non-Circular Pupils: Cat Eye The slit shape of the pupil found in many nocturnal animals, such as this cat, presumably allows more effective light reduction than a circular pupil.

Pupil Size Changes With Mean Luminance, Influencing Acuity (From Wyszecki and Stiles, 1982) Pupil diameter (mm) From Wyszecki and Stiles Log luminance (Trolands)

The Pointspread Function Is The Generalization of the Linespread

Astigmatism Measures The Orientation of the Pointspread Function

Chromatic aberration is a differences in optical focus that varies with wavelength Stimulus (B) Stimulus -0.3 0.3 Position

Chromatic Aberration Can Be Summarized By The Optical Power At Various Wavelengths; Very Constant Across People

Short wavelength linespread functions are much broader than middle wavelength -1 -0.5 0.5 1 0.1 0.2 0.3 0.4 580nm Relative intensity 430nm Position (deg)

Chromatic aberration also can be summarized in terms of the MTF at each wavelength

Chromatic and spherical aberration: MTF

Chromatic aberration can also be summarized by its effect on the linespread Function Wavelength (nm) Spatial position (deg)

Recent Advances In Adaptive Optics Getting to the Diffraction Limit

Retina Wavefront Hartmann-Shack Wavefront Sensor Senses The Local Planarity Of The Image Wavefront Using a Lenslet Array A key technology supplied by AOA is the wavefront sensor. The most commonly used approach is the Shack-Hartmann method. As shown in Figure 2, this approach is completely geometric in nature and so has no dependence on the coherence of the sensed optical beam. The incoming wavefront is broken into an array of spatial samples, called subapertures of the primary aperture, by a two dimensional array of lenslets. The subaperture sampled by each lenslet is brought to a focus at a known distance F behind each array. The lateral position of the focal spot depends on the local tilt of the incoming wavefront; a measurement of all the subaperture spot positions is therefore a measure of the gradient of the incoming wavefront. A two-dimensional integration process called reconstruction can then be used to estimate the shape of the original wavefront, and from there derive the correction signals for the deformable mirror.

Example H-S displacement images at the CCD sensor Artal, Guirao, Berrio & Williams Journal of Vision Example H-S displacement images at the CCD sensor Figure 3. Examples of Hartmann-Shack image in the naked eye (A) and in the eye with filled goggles (B).

Adaptive optics corrects for the optical distortions using deformable mirror devices http://www.aoainc.com/technologies/adaptiveandmicrooptics/aostutorial.html Light from a nominal point source above the atmosphere enters the primary aperture and is split between a camera and a wavefront sensor ( See Fig. 1). The sensor measures the wavefront distortion and controls a tilt mirror to stabilize the image and a deformable mirror which restores the image sharpness lost to atmospheric turbulence. The adaptive optics system technologies developed and delivered by AOA include adaptive wavefront compensation for optical systems and wavefront measurement. In recent years, the technology and practice of adaptive optics have become, if not commonplace, at least well-known in the astronomical community.

Wavefront phase corrector priniciple http://www.ctio.noao.edu/~atokovin/tutorial/intro.html

Deformable mirror arrays Compensate For the Measured Aberrations

Deform the mirror to compensate for the wavefront curvature Early deformable mirrors (DMs) consisted of discreet segments, each controlled by 3 piezoelectric actuators. Nowadays, a common technology is to bond a thin faceplate to an array of piezoelectric actuators (see the Figure). The actuators are not produced individually, but rather a multi-layer wafer of piezo-ceramic is separated into individual actuators.

Real deformable mirror arrays http://www.ctio.noao.edu/~atokovin/tutorial/part2/dm.html This type of DMs was developed primarily for military applications, they are expensive. Some examples can be found at the WEB pages of Xinetics or Turn, Ltd. Piezoelectric actuators have a hysteresis of about 10%. The maximum deformation (stroke) is limited by a saturation of the piezoelectric material (sometimes, the applied voltage is also limited). The deformable mirror of the Keck AO is shown below.

Hartmann-Shack wave-front sensors Point source Fig. 1. Hartmann–Shack wave-front sensors used to measure the eye’s aberrations at (a) the University of Rochester and (b) Bausch & Lomb. The light from the SLD serves as a beacon, forming a point source on the retina. Light reflected from the retina emerges through the eye’s pupil as an aberrated wavefront and is propagated through the system to the lenslet array, placed conjugate with the eye’s pupil. Each lenslet forms a focused spot on the CCD, yielding an array of spots that finely samples the pupil. The wave aberration is determined from the Hartmann–Shack image.

Adaptive Optics compensate for aberrations in the optical path, the MTF approaches the diffraction limit

The MTF approaches the diffraction limit

Adaptive optics should permit visualization of the retina at high spatial resolution – Not Yet Routine (Liang and Williams)

End Reading for next Tuesday Liang and Williams paper Roorda and Williams paper Who wants to lead the discussion? Anyone have other papers to discuss?

Application: Seeing The Arrangement of Cone Classes in the Human Eye ( Roorda and Williams) mm

Zernicke Polynomials (Not Harmonics) Are Used To Model Transmission Through The Lens The Zernike polynomials are a set of functions that are orthogonal over the unit circle. They are useful for describing the shape of an aberrated wavefront in the pupil of an optical system. Project idea: Implement a set of Matlab functions for these polynomials. Explain their use in optics characterization. Review the human literature pertaining to measurements of wavefront aberrations in the human eye.