1. ComputationalRadiometry
  2. 12h-MWIR-Well-fill.ipynb
Notebook %This notebook demonstrates the use of the workpackage template, replace with your own. \documentclass[english]{workpackage}[1996/06/02] % input the common preamble content (required by the ipnb2latex converter) \input{header.tex} % then follows the rest of the preamble to be placed before the begin document % this preamble content is special to the documentclass you defined above. \WPproject{} % project name \WPequipment{} % equipment name \WPsubject{MWIR sensor well fill calculations} % main heading \WPconclusions{} \WPclassification{} \WPdocauthor{CJ Willers} \WPcurrentpackdate{\today} \WPcurrentpacknumber{} % work package number \WPdocnumber{} % this doc number hosts all the work packages \WPprevpackdate{} % work package which this one supersedes \WPprevpacknumber{} % work package which this one supersedes \WPsuperpackdate{} % work package which comes after this one \WPsuperpacknumber{} % work package which comes after this one \WPdocontractdetails{false} \WPcontractname{} % contract name \WPorderno{} % contract order number \WPmilestonenumber{} % contract milestone number \WPmilestonetitle{} % contract milestone title \WPcontractline{} % contract milestone line number \WPdocECPnumber{} % ecp/ecr number \WPdistribution{} %and finally the document begin. \begin{document} \WPlayout
It is shown in the companion document to this analysis that the detector element irradiance is then \begin{eqnarray} E_{\lambda\textrm{det},\alpha} = \frac{\Phi_{\lambda\textrm{det},\alpha}}{A_d} &=& (\Omega_3 -\Omega_4 - \Omega_5 - \Omega_6 ) \tau_{\lambda o}\tau_{\lambda f} \cos^4\alpha L_{\lambda\textrm{scene}} \nonumber\\ &&+ (\Omega_3 -\Omega_4 - \Omega_5 - \Omega_6 )\tau_{\lambda f}(1 -\tau_{\lambda o}) L_{\lambda}(T_{\textrm{optics}})\nonumber\\ &&+ (\Omega_3 -\Omega_4 - \Omega_5 - \Omega_6 )\tau_{\lambda f} \rho_{\lambda n} \left[L_{\lambda}(T_{\textrm{optics}})-L_{\lambda}(T_{\textrm{cold}})\right] \nonumber\\ &&+ \Omega_3 (1 -\tau_{\lambda f}) L_{\lambda}(T_{\textrm{filter}}) \nonumber\\ &&+ \Omega_4 \tau_{\lambda f} \epsilon_{\lambda\textrm{a-obs}} L_{\lambda}(T_{\textrm{a-obs}}) \nonumber\\ &&+ \Omega_5 \tau_{\lambda f} \epsilon_{\lambda\textrm{c-obs}} L_{\lambda}(T_{\textrm{c-obs}}) \nonumber\\ &&+ \Omega_6 \tau_{\lambda f} \epsilon_{\lambda\textrm{v-obs}} L_{\lambda}(T_{\textrm{v-obs}}) \nonumber\\ &&+ \Omega_{2b}\tau_{\lambda f}\epsilon_{\lambda\textrm{barrel}} L_{\lambda}(T_{{\textrm{barrel}}})\nonumber\\ &&+ \Omega_{2a}\epsilon_{\lambda\textrm{barrel}} L_{\lambda}(T_{{\textrm{barrel}}})\nonumber\\ &&+ \Omega_{1}\epsilon_{\lambda\textrm{cold\;shield}} L_{\lambda}(T_{{\textrm{cold\;shield}}}), \end{eqnarray} where, $L_{\lambda}(T)$ is the spectral Planck-law radiation at temperature $T$, and $T_{\textrm{optics}}$ is the optics (window and optical elements) temperature, $T_{\textrm{filter}}$ is the filter temperature, $T_{\textrm{barrel}}$ is the optics barrel temperature, $T_{\textrm{cold\;shield}}$ is the cold shield temperature, $T_{\textrm{a-obs}}$ is the asymmetric obscuration temperature, $T_{\textrm{c-obs}}$ is the central obscuration temperature, $T_{\textrm{v-obs}}$ is the VNS obscuration temperature, $L_{\lambda}(T_{\textrm{cold}})$ is the radiance emanating from the inside of the cold shield, $\rho_{\lambda n}$ is the narcissis reflectance, $\epsilon_{\lambda\textrm{barrel}}$ is the barrel spectral emissivity, $\epsilon_{\lambda\textrm{a-obs}}$ is the asymmetric obscuration spectral emissivity, $\epsilon_{\lambda\textrm{c-obs}}$ is the central obscuration spectral emissivity, $\epsilon_{\lambda\textrm{c-obs}}$ is the VNS obscuration spectral emissivity, $\epsilon_{\lambda\textrm{cold\;shield}}$ is the cold shield spectral emissivity. The equivalent irradiance $E_{q\lambda\textrm{det},\alpha}$ can be calculated in photon rate terms by using photon rate radiance $L_{q\lambda}(T)$ in the above equation. The optics solid angle is given by \begin{equation} \Omega_3 = \pi\sin^2\theta = \pi(NA)^2 = \frac{\pi}{(2F_\sharp)^2} \end{equation} where $\theta$ is the half apex angle of the f-number cone. For small angles $\cos^4\alpha\approx\cos^2\alpha\approx 1$, then $L_{\lambda\textrm{scene}} = \tau_{\lambda a}L_{\lambda\textrm{target}} + L_{\lambda\textrm{path}}$, where $\tau_{\lambda a}$ is the atmospheric transmittance to the target, $L_{\lambda\textrm{target}}$ is the target radiance, and $L_{\lambda\textrm{path}}$ is the atmospheric path radiance.
\begin{equation} t_i = \frac{W_f}{100}\cdot \frac{ 4 W_c f^2_\textrm{no}} {A_d\,\eta\,\int_0^{\lambda_c} \pi L_q(T_1) d\lambda} \end{equation}