A Review of Optics Austin Roorda Ph D

A Review of Optics Austin Roorda, Ph. D. University of Houston College of Optometry

These slides were prepared by Austin Roorda, except where otherwise noted. Full permission is granted to anyone who would like to use any or all of these slides for educational purposes.

Geometrical Optics Relationships between pupil size, refractive error and blur

Optics of the eye: Depth of Focus 2 mm 4 mm 6 mm

Optics of the eye: Depth of Focused behind retina In focus Focused in front of retina 2 mm 4 mm 6 mm

7 mm pupil Bigger blur circle Courtesy of RA Applegate

2 mm pupil Smaller blur circle Courtesy of RA Applegate

Demonstration Role of Pupil Size and Defocus on Retinal Blur Draw a cross like this one on a page, hold it so close that is it completely out of focus, then squint. You should see the horizontal line become clear. The line becomes clear because you have made you have used your eyelids to make your effective pupil size smaller, thereby reducing the blur due to defocus on the retina image. Only the horizontal line appears clear because you have only reduced the blur in the horizontal direction.

Physical Optics The Wavefront

What is the Wavefront? parallel beam = plane wavefront converging beam = spherical wavefront

What is the Wavefront? parallel beam = plane wavefront ideal wavefront defocused wavefront

What is the Wavefront? parallel beam = plane wavefront ideal wavefront aberrated beam = irregular wavefront

What is the Wavefront? diverging beam = spherical wavefront ideal wavefront aberrated beam = irregular wavefront

The Wave Aberration

What is the Wave Aberration? diverging beam = spherical wavefront wave aberration

Wave Aberration of a Surface Wavefront Aberration mm (superior-inferior) 3 2 1 0 -1 -2 -3 -3 -2 -1 0 1 mm (right-left) 2 3

Diffraction

Diffraction “Any deviation of light rays from a rectilinear path which cannot be interpreted as reflection or refraction” Sommerfeld, ~ 1894

Fraunhofer Diffraction • Also called far-field diffraction • Occurs when the screen is held far from the aperture. • Occurs at the focal point of a lens!

Diffraction and Interference • diffraction causes light to bend perpendicular to the direction of the diffracting edge • interference due to the size of the aperture causes the diffracted light to have peaks and valleys

rectangular aperture square aperture

circular aperture Airy Disc

The Point Spread Function

The Point Spread Function, or PSF, is the image that an optical system forms of a point source. The point source is the most fundamental object, and forms the basis for any complex object. The PSF is analogous to the Impulse Response Function in electronics.

The Point Spread Function The PSF for a perfect optical system is the Airy disc, which is the Fraunhofer diffraction pattern for a circular pupil. Airy Disc

Airy Disk q

separatrion between Airy disk peak and 1 st min (minutes of arc 500 nm light) As the pupil size gets larger, the Airy disc gets smaller. 2. 5 2 1. 5 1 0. 5 0 1 2 3 4 5 pupil diameter (mm) 6 7 8

Point Spread Function vs. Pupil Size 1 mm 5 mm 2 mm 3 mm 6 mm 4 mm 7 mm

Small Pupil

Larger pupil

Point Spread Function vs. Pupil Size Perfect Eye 1 mm 5 mm 2 mm 3 mm 6 mm 4 mm 7 mm

Point Spread Function vs. Pupil Size Typical Eye 1 mm 2 mm 3 mm 4 mm pupil images followed by 5 mm psfs for changing pupil size 6 mm 7 mm

Demonstration Observe Your Own Point Spread Function

Resolution

Unresolved point sources Rayleigh resolution limit Resolved

uncorrected AO image of binary star k-Peg on the 3. 5 -m telescope at the Starfire Optical Range About 1000 times better than the eye!

Keck telescope: (10 m reflector) About 4500 times better than the eye! Wainscott

Convolution

Convolution

Simulated Images 20/20 letters 20/40 letters

MTF Modulation Transfer Function

low medium object: 100% contrast image 1 0 spatial frequency high

• The modulation transfer function (MTF) indicates the ability of an optical system to reproduce (transfer) various levels of detail (spatial frequencies) from the object to the image. • Its units are the ratio of image contrast over the object contrast as a function of spatial frequency. • It is the optical contribution to the contrast sensitivity function (CSF).

MTF: Cutoff Frequency cut-off frequency 1 mm 2 mm 4 mm 6 mm 8 mm modulation transfer 1 0. 5 Rule of thumb: cutoff frequency increases by ~30 c/d for each mm increase in pupil size 0 0 50 100 150 200 250 spatial frequency (c/deg) 300

Effect of Defocus on the MTF 450 nm 650 nm Charman and Jennings, 1976

PTF Phase Transfer Function

low medium object phase shift image 180 0 -180 spatial frequency high

Relationships Between Wave Aberration, PSF and MTF

The PSF is the Fourier Transform (FT) of the pupil function The MTF is the real part of the FT of the PSF The PTF is the imaginary part of the FT of the PSF

Adaptive Optics Flattens the Wave Aberration AO OFF AO ON

Other Metrics to Define Imagine Quality

Strehl Ratio diffraction-limited PSF Hdl actual PSF Heye

Retinal Sampling

Sampling by Foveal Cones Projected Image 20/20 letter Sampled Image 5 arc minutes

Sampling by Foveal Cones Projected Image 20/5 letter Sampled Image 5 arc minutes

Nyquist Sampling Theorem

Photoreceptor Sampling >> Spatial Frequency 1 I 0 nearly 100% transmitted

Photoreceptor Sampling = 2 x Spatial Frequency 1 I 0 nearly 100% transmitted

Photoreceptor Sampling = Spatial Frequency 1 I 0 nothing transmitted

Nyquist theorem: The maximum spatial frequency that can be detected is equal to ½ of the sampling frequency. foveal cone spacing ~ 120 samples/deg maximum spatial frequency: 60 cycles/deg (20/10 or 6/3 acuity)