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Equation Summary

General equations (index, refraction, mirrors, etc.):

OPL=ndρ=(n2n1n2+n1)2n1sinθ1=n2sinθ2sinθC=n2n1τ=tnω=nuγ=2αd(n1n)t=tτ

Power and focal length:

ϕ=(nn)C=(nn)RfE1ϕ=fFn=fRn

Newtonian equations (z, z′ measured from F, F′):

zn=fEmzn=mfE(zn)(zn)=fE2

Gaussian equations and imaging (z, z′ measured from P, P′):

zn=(1m)mfEzn=(1m)fEm=z/nz/n=ωωnz=nz+1fEΔz/nΔz/n=m1m2m¯=(nn)m2zPN=zPN=fF+fRmN=fFfR=nn

Gaussian reduction:

ϕ=ϕ1+ϕ2ϕ1ϕ2τdn=ϕ2ϕτdn=ϕ1ϕτBFD=fR+dFFD=fF+d

Thin lens:

ϕ=(n1)(C1C2)L=zz=(1m)2mfE

Afocal systems:

m=fE2fE1=f2f1m¯=nnm2Δz/nΔz/n=m2

Paraxial raytrace:

nu=nuyϕω=ωyϕy=y+uty=y+ωτ

FOV, stops and pupils:

f102_1.jpg

Vignetting:

Un:Half:Fully:a|y|+|y¯|a=|y¯|a|y¯||y|a|y|a|y|

Depth of focus and hyperfocal distance:

DOF±Bf/#W±B2NALH=fDBLNEARLH2

Magnifiers, telescopes and microscopes:

MP=250mmfMP=1m=fOBJfEYEmV=mOBJMPEYE

Dispersion:

v=V=nd1nFnCP=Pd,c=ndncnFnCn=sin[(αδMIN)/2]sin(α/2)

Thin prisms:

δ(n1)αΔ=δνɛ=PΔ=Pδνα1δ=(1ν2ν1)(ν1nd11)α2δ=(1ν2ν1)(ν2nd21)ɛδ=(P2P1ν2ν1)=ΔPΔν

Chromatic aberration and achromats:

δff=δϕϕ=1νTACH=rPνϕ1ϕ=ν1ν1ν2ϕ2ϕ=ν2ν1ν2δϕdCϕ=δfcdf=ΔPΔν

Surface sag:

s(r)r22Rs(r)=Cr21+(1(1+κ)C2r2)1/2

Radiometry and radiative transfer:

Ω=2π(1cosθ0)Ωπr02d2πθ02L=Mπ=ρEπΦ=LAΩE=πL4(1m)2(f/#)2=πL4(f/#W)2=πL(NA)2H=EΔT

Diffraction limited systems:

D=2.44λf/#WDf/#Winμm(λ=0.5μm)δz=±2λ(f/#)2δz±(f/#)2inμm(λ=0.5μm)
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