Lecture 29- Light flow through the eye

Question 1

What is a troland ?

Answer 1

measure of retinal illuminance- takes into account the seize of the pupil and luminance of the object

Question 2

What is the most expensive part of the data projector ?

looking at screen luminance of projected image

Answer 2

projection lens - which captures a lot of light from this slide and is projected to form an image on a screen- the screen is usually a lambertian screen - important seen equally bright to people in audience

Question 3

What is the intensity of light towards projection lens ?

Answer 3

area x luminance
then multiply by the solid angle (which lens subtends at the slide ) ( pi u2) - we have total light flux captured by this lens from this slide

Question 4

What happens to some of the total light flux ?

Answer 4

• will be lost by scatter and absorption within the lens

Question 5

So , what is the total light flux that is transmitted to image space ?

Answer 5

t (transmittance ) x light flux captured by the lens

Question 6

Where is the light flux distributed ?

Answer 6

over the area of the image , area of image a’ = area of object a x square of transverse magnification
***

Question 7

Why do you need a lot of light in this slide ?

Answer 7

to ensure the image seen in audience is of sufficient luminance

Question 8

What will the illuminance level in the plane of the screen ?

Answer 8

total luminous flux captured by lens and transferred to image space divided by area of image

Question 9

What does the the amount off light per unit are of this screen depends on ?

Answer 9

• brightness of this image which is L
• depends on size of lens - solid angle - lens subtends at the slide piu²
• how much light absorbed by this lens - t

Question 10

What happens if light is distributed over a small image ?

Answer 10

-will correspond to a high illuminance

Question 11

What happens if light is distributed over a large image (so large Magnification )?

Answer 11

• will correspond to a small illuminance

* ***

Question 12

What is the screen colour/light ?

Answer 12

usually white

-has a certain reflectance

Question 13

What are majority of the screen ?

Answer 13

lambertian surfaces

Question 14

Why are they lambertian surfaces ?

Answer 14

because they should appear to be equally bright wherever the subject is in the audience
-for e.g could be both perpendicular to the screen as well as at large angles subtended from lens

Question 15

What will the total light flux that is reflected back by the screen will be?

Answer 15

the total flux it receives x reflectance of screen

Question 16

What is the total flux emitted by a lambertian source of L’ - which is the luminance of a screen?

Answer 16

luminance x area of image x pi

Question 17

What is the formula for image size ?

Answer 17

A ‘ = A x M²

Question 18

Overall what will the luminance of the screen equal to (equation ) ?

Answer 18

L’ = TRsLu²(1/M2)

brighter slide- brighter luminance of screen
proportional u² - because its poroptional to the solid angle of which the light is captured by the lens then divided by the square of transverse mag - which means larger image - smaller luminance

Question 19

What is the luminance of the screen ?

Answer 19

L’

Question 20

How does image size affect screen luminance?

Answer 20

Let the reflectance of the screen be, Rs, and the luminance of projected image on the screen be, L’ . Since most screens are Lambertian, the total luminous flux reflected by the screen from an image of area, A’, equals pi x L’ x A’

Question 21

What is the troland ?

Answer 21

a measure of retinal illuminance

Question 22

Why was troland introduced ?

Answer 22

introduced to avoid the need to know light losses within each eye and parameters such as refractive index and image size

Question 23

What is the retinal illuminance equation in trolands ?

Answer 23

E (trolands) = PA(mm2)*L (cd/m2)

L- luminance of object
PA- area of pupil in mm²

Question 24

What is one troland ?

Answer 24

• the retinal illuminance which results when the eye uses a screen of luminance 1cd/m² through a pupil having an area of 1 mm²

for e.g
If the pupil area is 10 mm2, for example, then the same object luminance (i.e., 1 cd/m2) would generate a retinal illuminance of 10 trolands.

Question 25

Explain the pupil size and retinal illuminance via simple lens system :

Answer 25

• lens approximates pupil
• relationship of image and object in terms of light levels is virtually the same
  -light flux captured by the lens - luminous flux = ALpiu²
  -Light flux transmitted to image space: luminous flux’ = TALpiu² - the flux that is transmitted towards the retina
• Image size (mag) - nu x n’u’ = transverse magnification
  Mag - A’ = AM² WHERE M = nu/n’u’
• total flux transferred towards retina divide by area of image- E = TLPIu²/ M²

Question 26

What is the image illuminance for retina ?

Answer 26

E = TLPIu²/ M²

Question 27

What is the derivation of the retinal illuminance equation \?

Answer 27

• E = TLPIu²/ M²
• E = TLpi (n’/n)2(u’)2
• Let PA = pi x a (area of pupil)
• E = T(n’/f’)² (LPA)
• Retinal Illuminance (trolands) = LPA

Question 28

What is the actual change in image plane position ?

Answer 28

• difference between true image distance and focal lens very small - reason why can express u’ as the radius of the pupil of the eye divided by fovea length f’

Question 29

What is the summary of formulas ?

Answer 29

Illuminance (lm/m2)- amount of light per unit area of a given service recieved from a source of intensity I theta . - this formula captures both inverse square law and cosine law
E(lm/m2)= I cosθ/r²

-Luminance (lm/sr/m2) or (cd/m2)
L (cd/m2)= I /Acosθ
A - area of source projected onto a plane perpendicular to the direction of interest - Acosθ

-Lambertian sources / surfaces ?
, L= Io/A (constant)
- the luminance is constant and independent of the direction of measurement which means the surface appears to be equally bright irrespective of the direction is viewed at
-for illuminated lambertian surface
L= E x R/pi
A- area
L -luminance 
total luminous flux- which source emits = pi x LA

-Retinal Illuminance (td)- Retinal Illuminance, E(trolands) = LPA