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Resources / Tech Tools / Equations

EO Tech Tools Equations

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

Focal Length

Focal Length Calculator, equation 1
Focal Length Calculator, equation 2
Focal Length Calculator, equation 3
Focal Length Calculator, equation 4
Focal Length Calculator, equation 5
Focal Length Calculator, equation 6
Focal Length Calculator, equation 7
Focal Length Calculator, equation 8
Focal Length Calculator, equation 9
Focal Length Calculator, equation 10
Focal Length Calculator, equation 11
FOS Power of Surface 1
FIS Power of Surface 2
F Lens Power
nOS Object Space Index
nL Lens Index
nIS 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
fF Front Focal Point
fR Rear Focal Point

Gaussian Beam

Gaussian Beam Calculator, equation 1
Gaussian Beam Calculator, equation 2
Gaussian Beam Calculator, equation 3
Gaussian Beam Calculator, equation 4
Gaussian Beam Calculator, equation 5
Gaussian Beam Calculator, equation 6
? Wavelength
zR 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

Koehler Illumination Calculator, equation 1
Koehler Illumination Calculator, equation 2
Koehler Illumination Calculator, equation 3
Koehler Illumination Calculator, equation 4
Koehler Illumination Calculator, equation 5
Koehler Illumination Calculator, equation 6
Koehler Illumination Calculator, equation 7
d1 Source to Lens 1 Distance
d2 Lens 1 to Lens 2 Distance
d3 Lens 2 to Spot Diameter Distance
DL1 Diameter of Lens 1
DL2 Diameter of Lens 2
FL1 Focal Length of Lens 1
FL2 Focal Length of Lens 2
Dsource Source Diameter
Dspot Spot Diameter
NAinput Input Numerical Aperture
NAoutput Output Numerical Aperture

Laser Spot Size

Laser Spot Size Calculator, equation 1
DI Input Beam Diameter
DO Output Beam Diameter
?I Beam Divergence
L Working Distance

1951 USAF

1951 USAF Resolution Calculator, equation 1


SAG Calculator, equation 1
R Radius of Curvature
D Diameter

Simple Magnifier

Simple Magnifier Calculator, equation 1
Simple Magnifier Calculator, equation 2
MP Magnifying Power
FL Focal Length

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

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

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

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

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

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