Compare Telescopes

Compare the imaging performance of 2 telescopes for astrophotography.
Performance indicators are: pixel scale (res), FOV, extended object irradiance (eoi), point object irradiance (poi), etendue (e), pixel etendue (pe), pixel signal (ps) and object signal (os).
Version 1.3
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], default 100
aperture Diameter in inches [inch]
focal Length [mm], default 1000
F/ratio [float], default 10
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
Binning [1-9], 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
    

Etendue

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

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

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

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
    

History