1. Human Perception
2: Image Formation

2. Studying Reflections from the Eye
Imaging components of the eye
Light
enters pupil, which is bordered by the iris
is brought into focus by the cornea and lens
Passes through the transparent vitreous and retinal cell layers
2.2

3. Studying Reflections from the Eye
The beam-splitter
Measuring light reflected from the eye
2.3

4. Studying Reflections from the Eye
A modified ophthalmoscope
2.4

5. Studying Reflections from the Eye
What part of the eye reflects the image?
2.5

6. Studying Reflections from the Eye
Experimental measurements
Human eye
Looking at a fine line
Blurred by double passage
(Campbell & Gubisch 1966)
2.6

7. Linear Systems Methods
Retinal image formation
2.7

8. Linear Systems Methods
The principle of homogeneity
2.8

9. Linear Systems Methods
The principle of superposition
2.9

10. Linear Systems Methods
Linear transform: R=L(P)
Homogeneity: L(aP)=aL(P)
Superposition: L(P+P’)=L(P)+L(P’)
2.10

11. Linear Systems Methods
Application of homogeneity & superposition
2.11

12. Linear Systems Methods
Retinal image formation
R=LP
vector and matrix representation
2.12

13. Shift-Invariant Linear Transformations
Definition
2.13

14. Shift-Invariant Linear Transformations
Properties
The system matrix from the response to a single stimulus
The response to a harmonic function is a harmonic function at the same frequency
cos(2π f i/N)  sf cos(2π f i/N + a)
2.14

15. The Optical Quality of the Eye
Sinusoids and double passage
2.15

16. The Optical Quality of the Eye
Sinusoids and double passage
Image:
P=Σ cos(2π f i/N)
Measurement:
R=Σ (sf) 2 cos(2π f i/N)
Single pass at retina:
R’=Σ sf cos(2π f i/N)
2.16

17. The Optical Quality of the Eye
The linespread function of the human eye
2.17

18. The Optical Quality of the Eye
The linespread function of the human eye: an analytic approximation:
0.47exp(-3.3i2) exp(-0.93|i|)
2.18

19. The Optical Quality of the Eye
Examples of the effect of optical blurring
2.19

20. The Optical Quality of the Eye
Linespread function in frequency domain
2.20

21. The Optical Quality of the Eye
pointspread function
(A) a pointspread function
(B) the sum of two pointspreads
When the optics are shift-invariant, the image to any stimulus can be predicted from the pointspread function
2.21