Pixel Scale, or pixel resolution, is the solid angle that is projected on a single pixel.
It is measured in arcseconds per pixel,
pixel scale ["/pixel] = 206.265 [k"] * pixel size [μm/pixel] / focal length [mm]
With 206.265 the amount of arcseconds per radian / 1000 .
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.
angle_x ["] = camera_pixels_x [pixels] * pixel scale ["/pixel] angle_y ["] = camera_pixels_y [pixels] * pixel scale ["/pixel]
FOV is displayed in arcminutes
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
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.
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).
Point_Object_Irradiance_ratio = (ota 1 aperture area/ota 2 aperture area) * 1 / (focal ratio of ota 1/focal ratio of ota 2)^2
Pixel Etendue represents a measure of the size and angular spread of a beam of light onto a pixel.
Etendue is a system property of the OTA,
G = aperture_area * pi * NA^2. It is translated to a single pixel here.
Etendue is also known as light-gathering or light-collecting power.
pixel_etendue = aperture_area [mm^2] * pixel_scale^2 ["^2/pixel]
Classically we should use
aperture_area * pi * (pixel_scale/2)^2 instead. But for the ratio this does not matter.
Pixel Signal is the Pixel Etendue corrected for the sensor Quantum Efficiency and total optical system Transmittance losses.
pixel_signal = pixel_etendue * QE-factor * Transmittance-factor