Compare Telescopes

Compare the imaging performance of 2 telescopes for astrophotography.
Performance indicators are: pixel scale, FOV, extended object irradiance, point object irradiance, etendue and signal.
Version 1.0
Source code at https://github.com/d33psky/compare-telescopes/
This is the web version of the Python CLI program.


OTA 1 OTA 2
aperture Diameter in mm [mm]
aperture Diameter in inches [inch]
focal Length [mm]
F/ratio []
focal Reducer factor [float], default 1
central Obstruction ratio [0-1>, default 0
total Transmittance factor <0-1], default 1
Camera 1 Camera 2
Horizontal pixels [count], default 1000
Vertical pixels [count], default 1000
Pixel size [μm], default 3.8
Quantum efficiency factor [0-1], default 1
        

Performance indicators

Pixel Scale, or pixel resolution.

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

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

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

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
    

Pixel Etendue

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.

Formula:

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

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