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Back Matter
Abstract
This back matter contains the bibliography, index and author's biography.

Equation Summary

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

$\begin{array}{ll}OPL=nd& \text{ρ}={\left(\frac{{n}_{2}-{n}_{1}}{{n}_{2}+{n}_{1}}\right)}^{2}\\ {n}_{1}sin{\text{θ}}_{1}={n}_{2}sin{\text{θ}}_{2}& sin{\text{θ}}_{\text{C}}=\frac{{n}_{2}}{{n}_{1}}\\ \text{τ}=\frac{t}{n}& \text{ω}=nu\\ \text{γ}=2\text{α}& d\approx \left(\frac{n-1}{n}\right)t=t-\text{τ}\end{array}$

Power and focal length:

$\begin{array}{ll}\text{ϕ}=\left({n}^{\prime }-n\right)C=\frac{\left({n}^{\prime }-n\right)}{R}& {f}_{E}\equiv \frac{1}{\text{ϕ}}\end{array}=\frac{{f}_{F}}{n}=-\frac{{f}_{R}^{\prime }}{{n}^{\prime }}$

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

$\begin{array}{lll}\frac{z}{n}=\frac{{f}_{E}}{m}\phantom{\rule{3em}{0ex}}& \frac{{z}^{\prime }}{{n}^{\prime }}=-m{f}_{E}\phantom{\rule{3em}{0ex}}& \left(\frac{z}{n}\right)\end{array}\left(\frac{{z}^{\prime }}{{n}^{\prime }}\right)=-{f}_{E}^{2}$

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

$\begin{array}{lll}\frac{z}{n}=\frac{\left(1-m\right)}{m}{f}_{E}& \frac{{z}^{\prime }}{{n}^{\prime }}=\left(1-m\right){f}_{E}& m=\frac{{z}^{\prime }/{n}^{\prime }}{z/n}=\frac{\text{ω}}{{\text{ω}}^{\prime }}\\ \frac{{n}^{\prime }}{{z}^{\prime }}=\frac{n}{z}+\frac{1}{{f}_{E}}& \frac{\text{Δ}{z}^{\prime }/{n}^{\prime }}{\text{Δ}z/n}={m}_{1}{m}_{2}& \overline{m}=\left(\frac{{n}^{\prime }}{n}\right){m}^{2}\\ {z}_{PN}={z}_{PN}^{\prime }={f}_{F}+{f}_{R}^{\prime }& & {m}_{N}=-\frac{{f}_{F}}{{f}_{R}^{\prime }}=\frac{n}{{n}^{\prime }}\end{array}$

Gaussian reduction:

$\begin{array}{lll}\text{ϕ}={\text{ϕ}}_{1}+{\text{ϕ}}_{2}-{\text{ϕ}}_{1}{\text{ϕ}}_{2}\text{τ}& \frac{d}{n}=\frac{{\text{ϕ}}_{2}}{\text{ϕ}}\text{τ}& \frac{{d}^{\prime }}{{n}^{\prime }}=\frac{{\text{ϕ}}_{1}}{\text{ϕ}}\text{τ}\\ BFD={f}_{R}^{\prime }+{d}^{\prime }& & FFD={f}_{F}+d\end{array}$

Thin lens:

$\begin{array}{lll}\text{ϕ}=\left(n-1\right)\left({C}_{1}-{C}_{2}\right)& & L={z}^{\prime }-z=-\frac{{\left(1-m\right)}^{2}}{m}{f}_{E}\end{array}$

Afocal systems:

$\begin{array}{lll}m=-\frac{{f}_{E2}}{{f}_{E1}}=-\frac{{f}_{2}}{{f}_{1}}& \overline{m}=\frac{{n}^{\prime }}{n}{m}^{2}& \frac{\text{Δ}{z}^{\prime }/{n}^{\prime }}{\text{Δ}z/n}={m}^{2}\end{array}$

Paraxial raytrace:

$\begin{array}{ll}{n}^{\prime }{u}^{\prime }=nu-y\text{ϕ}& {\text{ω}}^{\prime }=\text{ω}-y\text{ϕ}\\ {y}^{\prime }=y+{u}^{\prime }{t}^{\prime }& {y}^{\prime }=y+{\text{ω}}^{\prime }{\text{τ}}^{\prime }\end{array}$

FOV, stops and pupils:

Vignetting:

$\begin{array}{lll}\text{Un}:& \text{Half}:& \text{Fully}:\\ a\ge |y|+|\overline{y}|& a=|\overline{y}|& a\le |\overline{y}|-|y|\\ & a\ge |y|& a\ge |y|\end{array}$

Depth of focus and hyperfocal distance:

$\begin{array}{ll}DOF\approx ±{B}^{\prime }f/{#}_{W}\approx ±\frac{{B}^{\prime }}{2NA}& \\ {L}_{H}=-\frac{fD}{{B}^{\prime }}& {L}_{NEAR}\approx -\frac{{L}_{H}}{2}\end{array}$

Magnifiers, telescopes and microscopes:

$\begin{array}{l}MP=\frac{250\text{mm}}{f}\\ MP=\frac{1}{m}=-\frac{{f}_{OBJ}}{{f}_{EYE}}\\ {m}_{V}={m}_{OBJ}M{P}_{EYE}\end{array}$

Dispersion:

$\begin{array}{ll}v=V=\frac{{n}_{d}-1}{{n}_{F}-{n}_{C}}& P={P}_{d,c}=\frac{{n}_{d}-{n}_{c}}{{n}_{F}-{n}_{C}}\\ n=\frac{sin\left[\left(\text{α}-{\text{δ}}_{MIN}\right)/2\right]}{sin\left(\text{α}/2\right)}& \end{array}$

Thin prisms:

$\begin{array}{lll}\text{δ}\approx -\left(n-1\right)\text{α}& \text{Δ}=\frac{\text{δ}}{\text{ν}}\phantom{\rule{2em}{0ex}}& \varepsilon =P\text{Δ}=P\frac{\text{δ}}{\text{ν}}\\ \frac{{\text{α}}_{1}}{\text{δ}}=\left(\frac{1}{{\text{ν}}_{2}-{\text{ν}}_{1}}\right)\left(\frac{{\text{ν}}_{1}}{{n}_{d1}-1}\right)& & \frac{{\text{α}}_{2}}{\text{δ}}=\left(\frac{1}{{\text{ν}}_{2}-{\text{ν}}_{1}}\right)\left(\frac{{\text{ν}}_{2}}{{n}_{d2}-1}\right)\\ \frac{\varepsilon }{\text{δ}}=\left(\frac{{P}_{2}-{P}_{1}}{{\text{ν}}_{2}-{\text{ν}}_{1}}\right)=\frac{\text{Δ}P}{\text{Δ}\text{ν}}& & \end{array}$

Chromatic aberration and achromats:

$\begin{array}{lll}\frac{\text{δ}f}{f}=\frac{\text{δ}\text{ϕ}}{\text{ϕ}}=\frac{1}{\text{ν}}& & T{A}_{CH}=\frac{{r}_{P}}{\text{ν}}\\ \frac{{\text{ϕ}}_{1}}{\text{ϕ}}=\frac{{\text{ν}}_{1}}{{\text{ν}}_{1}-{\text{ν}}_{2}}& & \frac{{\text{ϕ}}_{2}}{\text{ϕ}}=-\frac{{\text{ν}}_{2}}{{\text{ν}}_{1}-{\text{ν}}_{2}}\\ \frac{\text{δ}{\text{ϕ}}_{dC}}{\text{ϕ}}=\frac{\text{δ}{f}_{cd}}{f}=\frac{\text{Δ}P}{\text{Δ}\text{ν}}& & \end{array}$

Surface sag:

$\begin{array}{lll}s\left(r\right)\approx \frac{{r}^{2}}{2R}& & s\left(r\right)=\frac{C{r}^{2}}{1+{\left(1-\left(1+\text{κ}\right){C}^{2}{r}^{2}\right)}^{1/2}}\end{array}$

$\begin{array}{lll}\text{Ω}=2\text{π}\left({1-\text{cos}\text{θ}}_{0}\right)& & \text{Ω}\approx \frac{\text{π}{r}_{0}^{2}}{{d}^{2}}\approx {\text{π}\text{θ}}_{0}^{2}\\ L=\frac{M}{\text{π}}=\frac{\text{ρ}E}{\text{π}}& & \text{Φ}=LA\text{Ω}\\ {E}^{\prime }=\frac{\text{π}L}{4{\left(1-m\right)}^{2}{\left(f/#\right)}^{2}}=\frac{\text{π}L}{4{\left({f/#}_{W}\right)}^{2}}=\text{π}L{\left(NA\right)}^{2}& & \\ H={E}^{\prime }\text{Δ}T& & \end{array}$
$\begin{array}{lll}D=2.44\text{λ}f/{#}_{W}& D\approx f/{#}_{W}\text{in} \text{μ}\text{m}& \left(\text{λ}=0\text{.5}\text{μ}\text{m}\right)\\ \text{δ}z=±2\text{λ}{\left(f/#\right)}^{2}& \text{δ}z\approx ±{\left(f/#\right)}^{2}\text{in} \text{μ}\text{m}& \left(\text{λ}=0\text{.5}\text{μ}\text{m}\right)\end{array}$