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This section contains the equation summary, bibliography, index, and author biographies.

Equation Summary

Numerical aperture and f /# :

NA=nsinuf/#=fEPD

Rayleigh criterion:

ΔX=0.61λNA

Image height as a function of field angle:

h=ftanθ

Transverse ray error:

εy=1nuaWρyεx=1nuaWρx

Strehl ratio:

Strehl(12π2ω2)ω=RMSOPD

Wavefront aberration polynomial:

WIJKHIρJcosKθW(H,ρ,θ)=W020ρ2+W111Hρcosθ+W040ρ4+W131Hρ3cosθ+W222H2ρ2cos2θ+W220H2ρ2+W311H3ρcosθ+O(6)

Contrast:

Contrast=ImaxIminImax+Imin

Focal lengths of any two thin lens system:

fa=dffBFLfb=dBFLfBFLd

Zero-Petzval solution for two thin lenses:

fa=fb=fBFLd=(fBFL)2f

Two-mirror solution:

c1=BFLf2dfc2=BFL+df2dBFL

Schwarzchild solution:

d=2fc1=(51)fc2=(5+1)f

Aplanatic condition:

i=u

Bending and shape factors:

β=c1+c2c1c2C=ua+uauaua

Thin lens bending for minimum spherical:

c2c1=2n2n4n(2n+1)

Thin lens bending for minimum coma:

c2c1=(n2n1)n2

Achromatic doublet:

Φ=ϕ1+ϕ2ϕ1=ΦV1V1V2ϕ2=-ΦV2V1V2

Petzval sum:

jϕjnj

Thick lens power:

ϕ=ϕ1+ϕ2tn(ϕ1ϕ2)

Minimum clear aperture for no vignetting:

CAmin=|ya|+|yb|

Aspheric sag equation:

sag=z(r)=cr21+1(κ+1)(cr)2+dr4+er6+fr8+gr10+

Gradient index profiles:

n(r)=N00+N10r2+N20r4+n(z)=N00+N01z+N02z2+

Merit function:

ϕ=mi1wi2(citi)2

Athermalization condition:

dfLensdT=CTE1d1CTE2d2

Bireflectance scattering distribution function:

BSDF(θi,ϕi;θo,ϕo)=(LE)sr1

Sellmeier dispersion:

n(λ)=1+c1λ2λ2c4+c2λ2λ2c5+c3λ2λ2c6

Schott dispersion:

n(λ)=c1+c2λ2+c3λ2+c4λ4+c5λ6+c6c8

Snell’s law:

nsinθ=nsinθ

Paraxial ray tracing:

nu=nuyϕy=y+nu(dn)ϕ=c(nn)

Lens maker’s equation and linear magnification:

1s=1f+1sm=hh=fs+f

Thin lens power:

Φ=1f=(c1c2)(n1)

Diffraction gratings:

mλ=d[sin(θm)sin(θi)]λblaze=2dsinα

Sampling ratio:

Q=λ(f/#)pixelpitch

Lagrange invariant and étendue:

H=nu¯ynuy¯n2AΩ=π2H2Etendue=surfacedAaΩ

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