Lecture 29- Light flow through the eye Flashcards
What is a troland ?
measure of retinal illuminance- takes into account the seize of the pupil and luminance of the object
What is the most expensive part of the data projector ?
looking at screen luminance of projected image
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
What is the intensity of light towards projection lens ?
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
What happens to some of the total light flux ?
- will be lost by scatter and absorption within the lens
So , what is the total light flux that is transmitted to image space ?
t (transmittance ) x light flux captured by the lens
Where is the light flux distributed ?
over the area of the image , area of image a’ = area of object a x square of transverse magnification
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Why do you need a lot of light in this slide ?
to ensure the image seen in audience is of sufficient luminance
What will the illuminance level in the plane of the screen ?
total luminous flux captured by lens and transferred to image space divided by area of image
What does the the amount off light per unit are of this screen depends on ?
- 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
What happens if light is distributed over a small image ?
-will correspond to a high illuminance
What happens if light is distributed over a large image (so large Magnification )?
- will correspond to a small illuminance
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What is the screen colour/light ?
usually white
-has a certain reflectance
What are majority of the screen ?
lambertian surfaces
Why are they lambertian surfaces ?
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
What will the total light flux that is reflected back by the screen will be?
the total flux it receives x reflectance of screen
What is the total flux emitted by a lambertian source of L’ - which is the luminance of a screen?
luminance x area of image x pi
What is the formula for image size ?
A ‘ = A x M²
Overall what will the luminance of the screen equal to (equation ) ?
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
What is the luminance of the screen ?
L’
How does image size affect screen luminance?
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’
What is the troland ?
a measure of retinal illuminance
Why was troland introduced ?
introduced to avoid the need to know light losses within each eye and parameters such as refractive index and image size
What is the retinal illuminance equation in trolands ?
E (trolands) = PA(mm2)*L (cd/m2)
L- luminance of object
PA- area of pupil in mm²
What is one troland ?
- 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.
Explain the pupil size and retinal illuminance via simple lens system :
- 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
What is the image illuminance for retina ?
E = TLPIu²/ M²
What is the derivation of the retinal illuminance equation \?
- 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
What is the actual change in image plane position ?
- 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’
What is the summary of formulas ?
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
