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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

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a review of optics

A Review of Optics

Austin Roorda, Ph.D.

University of Houston College of Optometry

slide2

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.

slide3

Geometrical Optics

Relationships between pupil size, refractive error and blur

slide5

Optics of the eye: Depth of Focus

Focused behind retina

In focus

Focused in front of retina

2 mm

4 mm

6 mm

slide6

7 mm pupil

Bigger blur

circle

Courtesy of RA Applegate

slide7

2 mm pupil

Smaller blur

circle

Courtesy of RA Applegate

slide8

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.

slide9

Physical Optics

The Wavefront

what is the wavefront
What is the Wavefront?

parallel beam

=

plane wavefront

converging beam

=

spherical wavefront

what is the wavefront11
What is the Wavefront?

parallel beam

=

plane wavefront

ideal wavefront

defocused wavefront

what is the wavefront12
What is the Wavefront?

parallel beam

=

plane wavefront

ideal wavefront

aberrated beam

=

irregular wavefront

what is the wavefront13
What is the Wavefront?

diverging beam

=

spherical wavefront

aberrated beam

=

irregular wavefront

ideal wavefront

what is the wave aberration
What is the Wave Aberration?

diverging beam

=

spherical wavefront

wave aberration

wave aberration of a surface

Wavefront Aberration

3

2

1

mm (superior-inferior)

0

-1

-2

-3

-3

-2

-1

0

1

2

3

mm (right-left)

Wave Aberration of a Surface
diffraction
Diffraction

“Any deviation of light rays from a rectilinear path which cannot be interpreted as reflection or refraction”

Sommerfeld, ~ 1894

fraunhofer diffraction
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 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
slide21

rectangular aperture

square aperture

slide24

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.

slide25

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

slide27

As the pupil size gets larger, the Airy disc gets smaller.

2.5

2

1.5

separatrion between Airy disk peak and 1st min

(minutes of arc 500 nm light)

1

0.5

0

1

2

3

4

5

6

7

8

pupil diameter (mm)

point spread function vs pupil size
Point Spread Function vs. Pupil Size

1 mm

2 mm

3 mm

4 mm

5 mm

6 mm

7 mm

point spread function vs pupil size typical eye
Point Spread Function vs. Pupil SizeTypical Eye

1 mm

2 mm

3 mm

4 mm

pupil images

followed by

psfs for changing pupil size

5 mm

6 mm

7 mm

slide33

Demonstration

Observe Your Own Point Spread Function

slide35

Unresolved

point sources

Rayleigh

resolution

limit

Resolved

slide36

uncorrected

corrected

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!

slide37

Keck telescope:

(10 m reflector)

About 4500 times better than the eye!

Wainscott

simulated images
Simulated Images

20/20 letters

20/40 letters

slide41

MTF

Modulation Transfer

Function

slide42

low

medium

high

object:

100%

contrast

image

1

contrast

0

spatial frequency

slide43

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).
slide44

MTF: Cutoff Frequency

cut-off frequency

1 mm

1

2 mm

4 mm

Rule of thumb: cutoff frequency increases by ~30 c/d for each mm increase in pupil size

6 mm

8 mm

modulation transfer

0.5

0

0

50

100

150

200

250

300

spatial frequency (c/deg)

slide45

Effect of Defocus on the MTF

450 nm

650 nm

Charman and Jennings, 1976

slide46

PTF

Phase Transfer

Function

slide47

low

medium

high

object

image

180

phase shift

0

-180

spatial frequency

slide48

Relationships Between

Wave Aberration,

PSF and MTF

slide49

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

strehl ratio
Strehl Ratio

diffraction-limited PSF

Hdl

actual PSF

Heye

slide57

20/20 letter

5 arc minutes

Sampling by Foveal Cones

Projected Image

Sampled Image

slide58

20/5 letter

5 arc minutes

Sampling by Foveal Cones

Projected Image

Sampled Image

slide60

Photoreceptor Sampling >> Spatial Frequency

1

I

0

1

I

0

nearly 100% transmitted

slide63

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)