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