= Integral-field spectrograph volume scaling
With fixed <spectral resolving power>, <wavelength> interval, <diffraction grating> geometry, <photodetector> sampling and <collimator> <focal ratio>, a beam <diameter> scales as the <spaxel> width $\theta$, but the <optical camera> <focal length> stays fixed. A simple on-axis beam-envelope model therefore gives <collimator> and disperser volumes proportional to $\theta^3$ and <optical camera> volume proportional to $\theta^2$. With a fixed number of <spaxels> per <photodetector>, replication multiplies these volumes by $M\propto\theta^{-2}$. A fixed <photodetector> field adds transverse clearances and changes the small-$\theta$ limit; these exponents are not universal mechanical-volume laws.
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