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# 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)
 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

(12)
(13)
(14)
(15)
(16)
(17)
 ? 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

(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 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

(25)
 DI Input Beam Diameter DO Output Beam Diameter ?I Beam Divergence L Working Distance

(26)

### SAG

(27)
 R Radius of Curvature D Diameter

### Simple Magnifier

(28)
(29)
 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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