12.FINAL-Optics-Photometry+Radiometry
What's the overall summary of Diffuse Refelction - Lambert's cosine law?
Intensity reflected from an ideal diffuse surface is directly proportional to the cosine of the angle theta between the direction of the incident light and the surface normal. I = I n x cos theta
What happens if you change angles in Lamber's cosine law?
Intensity of reflection decreases.
What are the formulas for Wavelength, frequency and photon energy?
in vacuum - frequency = C / LAMBDA Photon energy E phot = hv = HC/ lambda # of photons = E total / E phot
What are the calculations that can compute light levels using spheres?
Proportion of light entering eye: 1) Angle ratio w /4π = A/rˆ2/ 4π 2) Area ratio = A/4πrˆ2
Sample Question: Q: A target has a luminance of 50 candelas per square meter and is viewed through a pupil diameter of 4mm. Retinal illumination is approximately? A) 1250 trolands B) 2500 trolands C) 625 trolands * D) 125 trolands
Pupil Area = π *2ˆ2 = 12.5 mm Object luminance =50 Retinal Illuminance = 50x 12.5 = 625 Trolands
What's the long way of doing the above calculation?
Pupil area = π * 1.25ˆ2 = 4.9 mmˆ2 = 4π*1ˆ2 = 12.6 mˆ2 Fraction of radiation entering pupil = 4.9e-6 / 12.6 = 0.4 e-6 Radiation a entering eye = 100 w * 0.4e-6 = 0.04 mw
What is Radiant Intensity of point source?
Emitted power per unit solid angle Units: Watts/ steradian
What is Radiant Power (Flux)?
Energy/second = Units = Joules/seconds = Watts
What is the typical way of quantify rate of light?
Flux or power in Joules/Seconds = Watt
When going from photopic to scotopic, what is the wavelength shift and what is it called?
Goes from 555 nm to 505 nm. This is called the Purkinje Shift
What is Lamber'ts cosine law of diffuse reflection?
Intensity is proportional to cosine angle reflection.
Photometry: What do you require to convert radiometric power into photometric power?
It requires knowledge of spectral sensitivity * the sensitivity of the human eye to light of a certain intensity varies strongly over the wavelength btwn 380 and 800 no * the conversion between radiometric and photometric unit is provided by eye sensitivity function (spectral sensitivity of the human eye)
What cones contribute to luminance at the fovea?
L and M Cones, not S cones
How much radiation enters your eyes from A) 100 W light bulb B) 1 milliwatt Laser ?
Lasers are collimated, and are dangerous 100 w Quick answer = D/4rˆ2 = 100watts * (2.5e-3/ 4*1)ˆ2 = 0.3906 ˆ-4 = 0.04 militants Laser = 1 mw Altough laser output is 100,000 times lower than the light bulb, the laser is 25 times more hazardous (1 mass vs. 0.04) IF ALL LIGHT ENTERS THE EYE
What is diffuse reflection? What's an example? What defines it?
Light that reflects diffusely Has the same luminance (brightness) in all directions Example: Matte, cosine Lambert Cosine Law of diffuse reflection
What is specular reflection? What's an example? What defines t?
Light that reflects specularly = luminance/brightness varies with different angles Example: Mirror Angle of Incident = angle of reflection
What is photometry?
Measures the human visual system's psychophysical response to light in terms of its perceived brightness to the human eye. It's all RELATIVE TO THE HUMAN EYE
What is Radiometry?
Set of techniques for measuring EM radiation, including visible light. They characterize the distribution of radiation's power (radiant energy) in space. opposed to photometric technique, which
What is the equation for 1 steradian?
W steradian (solid Angle) = A / rˆ2 1 steradian is the solid angle subtended by a region with area rˆ2 on the surface of a sphere of radius r The whole surface of a sphere subtends 4πrˆ2/rˆ2 = 4π
Are there different efficiency of light sources?
Yes, though luminance between a incandescent and fluorescent light bulb could be similar, the energy used for each are different.
What are photometric terms based off?
Retinal cone sensitivities (L-cones, S-Cones, and M-cones)
What are the wavelengths sensitivities for each of the cones?
S = 430 nm M= 535 nm L = 570 nm
At 555 nm, where Vlambda = 1, 1 Watt of radiant produces how many lumens?
680 * 1 * 1 = 680 lumens (or 683 lumens standard)
How do you calculate lumens?
680 x watts x relative spectral sensitivity response (V lambda)
What is the visible range of light?
400-700 no and 750-430 THz
What are the required lux for VA charts?
480 (for 150 cd/mˆ2 luminance)
What is the wavelength sensitivity of scotopic rod cons?
505 nm
What factors determine retinal illuminance?
1) Object luminance (affects how much light arrives at eye) 2) Pupil area (affects how much gets into eye) 3) Eye size & image magnification (affects how light is spread out on retina) TYPICALLY ONLY INCORPORATE 1 and 2
Radiometry and photometry are found everywhere with lighting and are frequently encountered at work and home
1. Soft white long life - should be 1125 / 75 watts 2. Traditional Snellen Chart - should be 480 lux 3. Art - 50-100 max lux allowed for print/drawings. 150 for oiled paintings
What is the rule of 60?
60 cm arc located 60 cm away subtends 60º
Recap of Last Lecture Q: When an emmetropic eye accomodates from far ( 0 diopter) to near (4 diopters) A) dioptric power of the eye increases B) spherical aberration remains the same C) Defocus changes from from positive to negative D) the pupil increases in diameter
A) dioptric powe of the eye increases Spherical aberrations (not defocus) changes from positive to negative
What is the relationship between the about of light of surface are to distance?
Amount of light per square meter of surface area is inversely proportional to distance ˆ2 E = illuminance I =Luminous intensity D = distance ˆ2
Sample Question: Q: Specularly reflected light: A) has the same color as the source of light B) Obeys the cosine law of reflection C) takes on the color of the surface D) has the same luminance in all directions
Answer = A
Sample Question: Q: Luminance of a surface or source can be measured in A) trolands B) Lumens per steradian c) Candelas per square meter D) Lumens
Answer: C
Sample Question: Q: luminous intensity of a point source is 75 lumens per steradian. The illumination falling on a surface 2 meters away is? A) 150 lumens/mˆ2 B) 75 lumens /mˆ2 C) 37.5 lumens /m ˆ2 d) 18.75 lumens/mˆ2
D) 75 / 2ˆ2 = 75/24 = 1.875
The science of Radiometry and Photometry can do what?
Describe the few equations necessary to measure and quantify light and radiation
Based prior answers, will a 75 watt bulb at 1 meter generate sufficient Illuminance?
Based on prior questions, No
CALCULATION NOT IN FINAL. BUT JUST IN CASE Example: What's the # of photons carried by a single visible short wavelength 400 nm?
C= 3e8 Thus Frequency = 3e8/400e-9 = 0.75 e 15 hz = 750 e 12 hz = 750 teraHz Photon energy = hv or hf = HC/lambda F = frequency H= Planck's constant 0.75e15 s-1 x 6.63e-34 J*s = 4.97 e -19 Joules / photon # photons 1 J of 400e-19 1/4.97 e-19 = 2.0 x 18 photons = A LOT OF PHOTONS
If you have 5 meters distance and 100 lumens/steradian, what is the luminance?
E = 100/5 = 4 lumens /mˆ2
Do all wavelengths stimulate vision equally?
No, green light has higher spectral sensitivity
What is the formula for retinal illuminance (Trolands)?
Object luminance (cd/mˆ2) * pupil area mmˆ2 Example: Object luminance = 100 cd/mˆ2 Pupil diameter = 4 mm Thus pupil area = π*2ˆ2 = 12.5 mmˆ2 Retinal illuminance = 100x12.5 = 1250 Trolands
Know the Zernicke mode. Each individual aberration has a unique impact to what?
On retinal image quality
What is irradiance?
Power arriving on surface of unit area Units: Watts /mˆ2
What is radiance of extended source?
Power per unit solid angle / unit surface area Units = Watts/STR/mˆ2
What are the different type of luminances?
Power vs. Power Density
What is a radian angle?
Radian angles are measured in 2D Circle circumference = 2πr Circle radius = r Circle area = π rˆ2
What is the difference between Radiance vs. luminance?
Radiance is the physical quantity related to light intensity: power of the light, spreading out in some solid angle, over some area Luminance is a photometric quantity which is basically the effect of radiance on our eyes. .f
What's the difference between Radiometry and Photometry?
Radiometry * has nothing to do with the eye's sensitivity. * It's the measurement of EM radiation * Radiant Power Photometry * has everything to do with eye's sensitivity. * It's the measurement of light and * Luminous power
Does a 75 watt bulb @ 1 m provide sufficient illuminance for an eye exam?
Recall: Illuminance = Luminous intensity / dˆ2 = total light output /4 π Therefore 75 W at 1 mister = Illuminance = total lumens / (4π x dˆ2) = 89.5 lux
What's the important relationship to understand between wavelength and amount of photons?
Shorter wavelengths (e.g. 400 nm) has higher energy per photon, so you need less photons to achieve a desired energy Meanwhile, longer wavelengths (e.g. 650) would require more photons as they emit less energy per photon in order to achieve the desired energy
Find the solid angle subtended at the center of the earth by NY State? (141,000).
Solid angle = area / rˆ2 141,000 / 6370ˆ2 = 0.0034748 str
What is the source spectrum?
Source spectrum is the amount of radiance as a function of wavelength. There are three examples in the slides - review them. Point is: 1) Fluoeresecent Lamp are the most energy efficient 2) Lasers are 1 wavelength 3) UV doesn't fall on the spectra 4) Incandescent is the least energy efficient since it falls on the more higher IR ranges.
What is the law of cosine?
This is a law used for when tilted surfaces E = I/dˆ2 * cos (theta)
What is the primary goal fo the eye?
To respond to EM radiation. Only a narrow range of wavelengths produce a visual response but high intensity of sources of EM energy can damage the eye.
How many types of reflections are there?
Two types 1) Specular reflection 2) Diffuse refelctions
Example of steradian calculation Calculate the solid angle subtended at the center of the earth by the US
US = 9.82 million square kilometers Earth Radius = 6370km solid angle = Area / rˆ2 Area = 9.82 million square km / (6370 km) ˆ2 = 0.242
