dp0-p4
Optical design of NIR-LFC
NIR-LFC has been fully packaged by placing an objective lens in a
certain position (BL, image sensor to objective lens
distance) that covers the target object distance from 60 mm to 250 mm.
Since the MLA project the objective lens image in LFC, an image-side
depth-of-field (DOF) of an objective lens and an object-side DoF of MLA
are matched at position a from the MLA plane. Since the MLA project the
objective lens image in LFC, an image-side DOF of objective lens and an
object-side DOF of MLA are matched at position a from MLA. The
corresponding image-side depth-of-field DOF range of objective lens are
denoted by a+ and a- planes.
Therefore, the object-side DOF and its corresponding DOF range, i.e.,
the maximum and minimum object position
(AL+ and
AL-) with fOBJ can be
calculated using the object-side DOF range of MLA (a+and a-).
A general concept to determine when a lens is in-focus or out-of-focus
is to use the effective resolution of the imaging system. An effective
resolution ratio (ERR) is defined by the ratio of effective resolution
(Re) and total resolution (Rt), and each
of Re and Rt are related to effective
pixel size (s), minimal size of a projected point (s0),
and a single pixel size (p). DI denotes total image
sensor size.
\begin{equation}
R_{e}=\frac{D_{I}}{\max\left[\left|s\right|,s_{0}\right]},R_{t}=\frac{D_{I}}{p},\ \nonumber \\
\end{equation}\begin{equation}
ERR=\ \frac{R_{e}}{R_{t}}=\frac{p}{\max[\left|s\right|,s_{0}]}\nonumber \\
\end{equation}
An ERR of LFC (ERRLFC) is determined by the image plane
distance (B) and distance from image plane at a given p, microlens
diameter (DMLA), and microlens focal length
(fMLA),
\begin{equation}
\text{ER}R_{\text{LFC}}=\frac{1}{|v|}\bullet\frac{p}{\max\left[\left|D_{\text{MLA}}\left(\frac{B}{f_{\text{MLA}}}-\frac{1}{v}-1\right)\right|,s_{0}\right]},\ \left(\text{for~{}}\left|v\right|\geq 1\right)\nonumber \\
\end{equation}
A virtual depth, i.e., ratio of a and B, (v = |a|/B)
is inversely proportional to ERRLFC. From the above
equations, the object-side DOF range of MLA (a+ and
a-) are determined as,
\begin{equation}
a^{-}=[\frac{1}{f_{\text{MLA}}}-\frac{1}{B}\left(1-\frac{s_{0}}{D_{\text{MLA}}}\right)]^{-1},\ \ a^{+}=[\frac{1}{f_{\text{MLA}}}-\frac{1}{B}\left(1+\frac{s_{0}}{D_{\text{MLA}}}\right)]^{-1}.\nonumber \\
\end{equation}
The image-side DOF range of LFC (DOFIS-LFC) and
a++ are calculated from
ERR-LFC, i.e., an ERR value at
a- position.
\begin{equation}
\text{ER}R_{\text{LFc}}^{-}=\left|\frac{B}{a^{-}}\right|\bullet\frac{p}{\max\left[\left|D_{\text{MLA}}\left(\frac{B}{f_{\text{MLA}}}-\frac{B}{a^{-}}-1\right)\right|,s_{0}\right]},\nonumber \\
\end{equation}\begin{equation}
\text{Do}F_{IS-LFC}=\frac{1}{\text{ER}R_{\text{LFC}}^{-}}\bullet\frac{2pN}{\left|\frac{B}{f_{\text{MLA}}}-1\right|}=\ a^{++}-a^{-},\nonumber \\
\end{equation}\begin{equation}
a^{++}=a^{-}+DoF_{IS-LFC}\nonumber \\
\end{equation}
Finally, minimum and maximum object distance, i.e.,
AL- and
AL+, are determined by using the thin
lens equation of calculated a-, a++,
fOBL, and an objective lens position from IP
(BL). The DOF range of LFC (DOFLFC),
i.e., object-side DOF range of objective lens, is the difference between
maximum objective distance and minimum objective distance.
\begin{equation}
A_{L}^{-}=[\frac{1}{f_{\text{OBJ}}}-\frac{1}{\left(B_{L}-{(a}^{-}-B)\right)}]^{-1},A_{L}^{+}=[\frac{1}{f_{\text{OBJ}}}-\frac{1}{\left(B_{L}-{(a}^{++}-B)\right)}]^{-1}\nonumber \\
\end{equation}\begin{equation}
\text{Do}F_{\text{LFC}}=A_{L}^{+}-A_{L}^{-}\nonumber \\
\end{equation}