EO Tech Tools Equations

Equations and corresponding legends for each of our EO Tech Tools.

Focal Length

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

F_OS	Power of Surface 1
F_IS	Power of Surface 2
F	Lens Power
n_OS	Object Space Index
n_L	Lens Index
n_IS	Image Space Index
R₁	Radius of Surface 1
R₂	Radius of Surface 2
CT	Center Thickness
P	Primary Principle Point
P'	Secondary Principle Point
EFL	Effective Focal Length
BFL	Back Focal Length
FFL	Front Focal Length
NPS	Nodal Point Shift
f_F	Front Focal Point
f_R	Rear Focal Point

Gaussian Beam

(12)

(13)

(14)

(15)

(16)

(17)

?	Wavelength
z_R	Rayleigh Range
z	Axial Distance
?(z)	Half Beam Diameter
?₀	Beam Waist
b	Confocal Parameter
?_R	Rayleigh Half Diameter
R(z)	Radius of Curvature
?	Half Angle Divergence

Koehler Illumination

(18)

(19)

(20)

(21)

(22)

(23)

(24)

d₁	Source to Lens 1 Distance
d₂	Lens 1 to Lens 2 Distance
d₃	Lens 2 to Spot Diameter Distance
D_L1	Diameter of Lens 1
D_L2	Diameter of Lens 2
F_L1	Focal Length of Lens 1
F_L2	Focal Length of Lens 2
D_source	Source Diameter
D_spot	Spot Diameter
NA_input	Input Numerical Aperture
NA_output	Output Numerical Aperture

Laser Spot Size

(25)

D_I	Input Beam Diameter
D_O	Output Beam Diameter
?_I	Beam Divergence
L	Working Distance

1951 USAF

(26)

SAG

(27)

R	Radius of Curvature
D	Diameter

Simple Magnifier

(28)

(29)

MP	Magnifying Power
FL	Focal Length

Focal Length Calculator

Ease integration of simple lenses into optical assemblies by providing lens radii, index of refraction, and center thickness.

Gaussian Beams Calculator

Use our Gaussian Beams Calculator to determine beam spot size in free space applications.

Koehler Illumination Calculator

Determine how to configure a source and two lenses into a Koehler Illumination setup with this easy-to-follow calculator.

1951 USAF Resolution Calculator

Input Group and Element Numbers to determine limiting resolution in terms of line pairs per millimeter of an imaging application setup.

SAG Calculator

Determine sag of a surface based on radius of curvature and diameter with this simple SAG Calculator.

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