Photometry
Calculating angle in radians
s/r s - arc lengths of a circle r - radius of the circle
Viewpoint Luminance Conceptual Example
In both cases, illuminance is the same, luminance differs
F in
Incident flux
Expression for image illuminance of a NON-perfect system
Includes transmittance
Retinal Illuminance (Et)
When viewing an object, the retina becomes illuminated non-SI is the troland (1 nt = 1 mm^2)
How do we calculate luminous exitance?
X = F out / A F out - exiting flux A - area of the surface SI is lux
Radiant Power SI
Watt (W) 1 W = 1 J/s
SI for Illuminance
lux (1 lx = 1 lm/m^2)
SI for Luminance (L)
nit (1 nt = 1 cd/m^2 = 1 lm/m^2 sr)
E
Illuminance
Bandwidth
Range of wavelengths where more than 50% of the light is transmitted
Equation for retinal illuminance
Et = Lo*Aent Lo - luminance of the object Aent - Area of the entrance pupil
Conservation of luminance
If a perfect system is in air, the luminance of the image equals the luminance of the object Lo = Li In a not perfect system, Li is NEVER greater than Lo
Projected area (Ap)
If an object is tiled an angle, the area that is viewed will be smaller Ap = Acos0 (on formula sheet)
How do we calculate luminance?
L = I/Ap I - intensity Ap - Projected area of the source
Equation for contrast (on equation sheet)
Lmax is simply the luminance of the light area and Lmin is the luminance of the dark area
SI from Luminous Flux
Lumen (lm)
X
Luminous exitance
How does luminous intensity differ from luminous flux?
Luminous flux emits light isotropically, luminous intensity tells us how much light is emitted in a given direction
Luminous flux vs Luminous intensity
Luminous flux tells us about the total amount of light emitted by a source in general, luminous intensity tells us how bright a beam of light is
I
Luminous intensity
Lambert's Law (given equation)
Luminous intensity of a perfectly diffuse source falls off with the cosine of the tilt angle
SI of Radiant Power
Watts or W
Luminous exitance for a perfectly diffuse system (equation)?
X = L(pie*sr) Steradians are included so the equation is dimensionally correct
Luminous exitance for a perfectly diffuse system (on equation sheet)
X = L(π sr)
If the light incident on the surface comes from a point source with intensity I, the illuminance of the surface decreases as the distance from the surface to the point source R ______________ (increases/decreases)
increases E = [ I cos 0 * sr ] / R^2 sr are explicitly included so the equation is dimensionally correct (gives units of lux) The main prompt is an example of the inverse square law
F
luminous flux
SI for luminous exitance (X)?
lux
Radiometry vs. Photometry
radiometry- techniques for measuring ALL electromagnetic radiation, whether we see it or not photometry- PERCEIVED brightness to human eye, ONLY visible light
What unit do we use for retinal illuminance (Et)? (considered a non-SI unit)
troland (1 nt = 1 mm^2)
Wavelength the eye is most sensitive to under scotopic conditions
507 nm
Et
Retinal illuminance
L
luminance
Radiometric unit for energy
Joule (j)
Equation for Illuminance
E = Fin/A = 1 lm/1 m^2 = 1 lx
Area of a sphere
4πR^2
Solid angle
w - ratio of the area (A) on a surface of a sphere to the square of the spheres radius (R^2) w = A / R^2 (on formula sheet) Units are steradians (sr)
Blackness is defined as what percentage of reflectance?
0%
SI of Luminous Intensity
1 cd = 1 lm/sr
What is the illuminance produced by 1 lm of luminous flux and is incident on a 1 m^2 surface?
1 lux 1 lm / 1 m^2
Conversion of radians to degrees
180 / (π*rad)
Circumference of a circle formula
2πr
Wavelength the eye is most sensitive to under photopic conditions
555 nm (yellow-green)
Isotropically
Equal intensity in all directions
How are reflectance and transmittance often expressed?
As a decimal or percentage (just multiply by 100)
Broadband filter
A filter that allows a greater range in wavelengths
Narrowband filter
A filter that only allows a certain color through
The luminance of a _______________________________ source does not depend on direction.
A perfectly diffuse source For a perfect imaging system in air, luminance is a conserved quantity
Perfectly diffuse source
A source that has the same luminance in all directions
Blackbody radiators
An EM radiation source that has a continuous radiation spectrium
Computing luminous intensity from luminous flux
Divide luminous flux (F) by the solid angle w F/w
How does luminous exitance compare to illuminance?
Both have the same unit of lux Illuminance deals with light incident on the surface Luminous exitance deals with light emitted from a surface
How are neutral density filters characterized?
By their optical density (OD)
Why do we use photometric quantities? (2 reasons)
Radiometrics is all the wavelengths, while photometrics is only the wavelengths the eye can see Photometry measures subjective brightness of the human visual
Transmittance (t)
Ratio between exiting and incident fluxes if surface transmits light t = F out / F in = X/E
Reflectance (p)
Ratio between the exiting and incident fluxes if surface reflects light p = F out / F in = X/E
If given a single source emitting a certain amount of lumens at one wavelength and a second amount of lumens at a different wavelength, how do you find total flux? (example picture)
Simply add the individual fluxes together
Example: A point source has an isotropic luminous intensity of 1 cd. How many lumens is the source emitting?
Since light is being emitted in all directions, w is the total solid angle subtended by a sphere, or 4π sr
What is the optical density if two neutral density filters are placed in combination?
Take the sum or their OD's
Luminance (L)
Tells us how bright a source of light appears to an observer SI is nit (1 nt = 1 cd/m^2 = 1 lm/m^2 sr)
Luminous Flux (F)
Tells us how much energy per unit time is emitted by a light source as perceived by the eye. SI unit is lumen (lm)
Luminous Exitance (X)
Tells us how much luminous flux exits a surface.
Illuminance (E)
Tells us how much luminous flux is incident on a surface. SI is lux (1 lx = 1 lm/m^2)
Luminous Intensity (I)
Tells us how much luminous flux per unit solid angle (in steradians or sr) is emitted by a light source. SI is candela (1 cd = 1 lm/sr)
Radiant Power
The amount of energy per time emitted by a light source, without taking the sensitivity of the eye into account SI is Watts or W
Blackbody radiator relationship with temperature
The peak emitted wavelength is inversely proportional to the temperature
How do you convert radiant power (J) to luminous flux (F) under photopic conditions?
To find V, use the graph to find the relative luminous efficiency from the given wavelength
Neutral density filter
Transmits all wavelengths equally Simply darkens the image, without color distortion
How do you convert radiant power (J) to luminous flux (F) under scotopic conditions?
Uses V' so denote scotopic