Access to eBooks is limited to institutions that have purchased or currently subscribe to the SPIE eBooks program. eBooks are not available via an individual subscription. SPIE books (print and digital) may be purchased individually on SPIE.Org.

Contact your librarian to recommend SPIE eBooks for your organization.
Ebook Topic:
Back Matter
Abstract
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

TOPIC

SHARE
Back to Top