Pixel Scale, or pixel resolution, is the solid angle that is projected on a single pixel.
It is measured in arcseconds per pixel, ["/pixel].
Formula:
pixel scale ["/pixel] = 206.265 [k"] * pixel size [μm/pixel] / focal length [mm]
With 206.265 the amount of arcseconds per radian / 1000 .
And arcseconds per radian = (360 / (2 * pi)) * 60 * 60 = 206264.80624709635515795...
FOV, Field Of View, is the solid angle that is projected on the camera sensor.
Formula:
angle_x ["] = camera_pixels_x [pixels] * pixel scale ["/pixel]
angle_y ["] = camera_pixels_y [pixels] * pixel scale ["/pixel]
FOV is displayed in arcminutes [']=["/60].
Extended Object Irradiance is the radiant flux (power) received by the sensor per unit area of an extended object.
Extended Object Irradiance is measured in [W/m^2].
We do not compute the irradiance itself because the ratio suffices and that varies as the inverse square of the focal ratio.
Aperture size alone does not matter for Extended Object Irradiance, only focal ratio does. (Aperture size does matter for Point Object Irradiance).
An extended object is anything that is not a point source, where a point source can be a star or anything else close to the size of the angular PSF projected onto the sky.
Formula:
Extended_Object_Irradiance_ratio = 1 / (focal ratio of ota 1/focal ratio of ota 2)^2
The Extended Object Irradiance is also known as the Speed of a film camera where an f/4 is twice as fast as an f/5.6, meaning you need only half the time.
Point Object Irradiance is the radiant flux (power) received by the sensor per unit area of a point object. For point objects such as stars the image irradiance varies as the aperture area ratio and the inverse square of the focal ratio. Aperture size matters for Point Object Irradiance, as well as focal ratio. (Aperture size alone does not for Extended Object Irradiance).
Formula:
Point_Object_Irradiance_ratio = (ota 1 aperture area/ota 2 aperture area) * 1 / (focal ratio of ota 1/focal ratio of ota 2)^2
Etendue is a measure of the flux gathering capability of the optical system onto the sensor. It is a purely geometric quantity.
Formula:
etendue = aperture_area [m^2] * FOV ["^2]
Pixel Etendue is the etendue for a single pixel. It represents the light-gathering power of a single pixel.
Formula:
pixel_etendue = aperture_area [mm^2] * pixel_scale^2 ["^2]
Pixel Signal is the Pixel Etendue corrected for the sensor Quantum Efficiency and total optical system Transmittance losses.
Formula:
pixel_signal = pixel_etendue * QE-factor * Transmittance-factor
Object Signal is based on the Etendue of an extended object that fits in the FOV of both scopes, corrected for the sensor Quantum Efficiency and total optical system Transmittance losses.
Formula: object_signal = aperture_area [m^2] * QE-factor * Transmittance_factor