# Advice needed for exposure time computation for galaxies

• A
In summary, the exposure time needed for an extended object is the product of the electron count multiplied by the area in arc seconds.
I am trying to compute the exposure time needed for an extended object (galaxy), in python.
I have found the following formulas:
Exposure time app # press the help button at the bottom of the calculator for the formulas used
Exposure time calc

Let's take for example the M33 galaxy. It has a surface mag of 23 mag/arcsec^2 and the dimension in arc minutes 73 x 45 or 4380 x 2700 arc seconds.
• What I am having trouble is understanding how to choose the 'n' value, respectively the radius value? Should I choose an arbitrary value? Does the radius mean the sample of pixels from the 23 mag faint spiral arms?
• I don't understand how to calculate the solid angle Omega_i for M33 galaxy. It seems the solid angle is somehow related to the the 'n' value from the first link? The formulas seem to be equivalent
Here is a sample from my code:

exposure time function:
def time(self):

# k1,k2 = flux/photon energy
# flux in W/m^2/nm
# photon energy in W*sec
# filter bandwidth in nm
# telescope aperture in m^2
# mag in mag/arcsec^2
# image scale in arc sec/pixel
k1 = util.flux(self.targetMagnitude, self.angle, self.typeOfBand, self.pressure, self.temperature)[0] / util.PhotonEnergy(self.typeOfBand)
k2 = util.flux(self.skyMagnitude, self.angle, self.typeOfBand, self.pressure, self.temperature)[0] / util.PhotonEnergy(self.typeOfBand)

radius = 10 # arc sec
pixelSurface = self.imageScale**2

self.targetElectronsSec = self.QE * k1 * self.filterBandwidth * self.effectiveAperture
self.skyElectronsSec = self.QE * k2  * self.filterBandwidth * self.effectiveAperture * self.imageScale

#solve the  equation for T
A = self.targetElectronsSec**2
B = -self.SNR**2 * (self.targetElectronsSec + npix*self.skyElectronsSec + npix*self.darkCurrent)
C = -self.SNR**2 * npix * self.readNoise**2
T = (-B + np.sqrt(B**2 - 4 * A * C)) / (2 * A) #returns seconds
return {'time':T}

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What I am having trouble is understanding how to choose the 'n' value, respectively the radius value? Should I choose an arbitrary value? Does the radius mean the sample of pixels from the 23 mag faint spiral arms?
Looking at the equation below the calculator, ##n## only appears in the noise terms for the sky, dark current, and readout, so it doesn't appear to have anything to do with the target. But playing around with it seems to show that ##n## only affects the target signal, which is odd. It appears that ##n## counters poor seeing. That is, increasing ##n## so that it is above the seeing will get you the full signal from the target. If ##n## is less than the seeing then you'll get less signal (e-/s). I just don't exactly know what this equation means: ##n=π(\frac{radius}{scale})^2##

I don't understand how to calculate the solid angle Omega_i for M33 galaxy. It seems the solid angle is somehow related to the the 'n' value from the first link? The formulas seem to be equivalent
I think the solid angle refers to the solid angle for each pixel (or group of pixels if binning), as it is labeled as: solid angle subtended by the integration element.

I believe an 'integration element' is a pixel or pixel group.

Drakkith said:
Looking at the equation below the calculator, ##n## only appears in the noise terms for the sky, dark current, and readout, so it doesn't appear to have anything to do with the target. But playing around with it seems to show that ##n## only affects the target signal, which is odd. It appears that ##n## counters poor seeing. That is, increasing ##n## so that it is above the seeing will get you the full signal from the target. If ##n## is less than the seeing then you'll get less signal (e-/s). I just don't exactly know what this equation means: ##n=π(\frac{radius}{scale})^2##I think the solid angle refers to the solid angle for each pixel (or group of pixels if binning), as it is labeled as: solid angle subtended by the integration element.

I believe an 'integration element' is a pixel or pixel group.
Signal - help I did found a help file for an older calculator.
So, for extended objects the electron counts are multiplied by the area of a pixel in arc seconds. For this we use the plate scale, that determines the size of the pixel in arc seconds. If my plate scale is 0.5 arc seconds per pixel, and the CCD pixels are square, we multiply the electron count by image_scale^2.

timmdeeg and Drakkith

## What factors should I consider when determining the exposure time for galaxy imaging?

When determining the exposure time for galaxy imaging, consider factors such as the brightness of the galaxy, the sensitivity of your camera, the light pollution in your observing location, the aperture of your telescope, and the desired signal-to-noise ratio (SNR). These factors will influence how long you need to expose to capture sufficient detail without overexposing the image.

## How does light pollution affect exposure time for galaxy imaging?

Light pollution significantly affects exposure time by increasing the background sky brightness, which can drown out faint details in the galaxy. In areas with high light pollution, longer exposure times may be required to achieve a good SNR, but this also increases the risk of overexposing the background. Using light pollution filters can help mitigate this effect.

## What is the role of the signal-to-noise ratio (SNR) in determining exposure time?

The signal-to-noise ratio (SNR) is crucial in determining exposure time because it measures the quality of the captured signal relative to the background noise. A higher SNR means better image quality with more visible details. To achieve a high SNR, longer exposure times are often needed, but this must be balanced against factors like sky conditions and equipment limitations.

## How can I calculate the optimal exposure time for my specific equipment and observing conditions?

To calculate the optimal exposure time, you can use the following steps: 1) Measure the sky background level in a short test exposure, 2) Determine the read noise and dark current of your camera, 3) Estimate the desired SNR based on your imaging goals, and 4) Use the formula: Exposure Time = (Desired SNR^2 * (Read Noise^2 + Sky Background)) / (Galaxy Signal). Alternatively, use online exposure calculators tailored to astrophotography.

## Is it better to take a single long exposure or multiple shorter exposures when imaging galaxies?

It is generally better to take multiple shorter exposures rather than a single long exposure. This approach helps mitigate issues like tracking errors, satellite trails, and cosmic rays. By stacking multiple shorter exposures, you can improve the overall SNR and reduce noise, resulting in a clearer and more detailed final image.

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