Aperture Photometry Optimizer

Author: Michael Newberry, Ph.D., Mirametrics, Inc.

This form calculates and graphs Signal to Noise Ratio (SNR) and Magnitude Error as a function of radius for aperture photometry of a point source. Use it for estimating the optimal aperture and loss of precision for a non-optimal aperture. Click [Save] to save parameters, click [Load] to fetch them. When using this form the first time, you can use [Load] to get sample parameters.   [Submit Comments

Camera
Pixel Size

microns
Binning

 
Readout Noise

electrons
Gain

e- / ADU
Temp

° C
T(doubling)

° C
T(ref)

° C
Dark Current

pA/cm^2 @ Tref
Instrument
Focal Length

mm
Diameter

mm
Secondary

diameter, mm
Efficiency

percent
Bandpass
Name

 
Filter Factor

percent (100%)
QE

percent
Extinction

mags @ zenith
Airmass

zenith = 1.0
Observations
Object Mag

magnitude
Exp Time

seconds
Seeing

FWHM, arcsec
Sky Mag

mag / arcsec^2
 

Notes on the graph and calculations:
  • Click [Update Results] to update both the graph and calculated quantities.
  • All results are shown in units of binned pixels
Magnitude Error vs. Aperture Radius
       Choose plot:   Magnitude Error   SNR
Mark reference at
Set the range of aperture radius for all calculations:
Minimum Radius

binned pixels

Maximum Radius

binned pixels
 

Calculated Quantities
Point Source: SNR

 
1-Sigma

+/- magnitudes
   
Detector: Dark Current

e- / s / pix
Base Noise

e- / pix
Image Scale

arcsec / pix
Object Flux

ADU / s
Background: Sky Flux

ADU / s / pix
Total BG Flux

ADU / s / pix
Total BG SNR

 
Sky / BG

 
Measurement: Aperture

x FWHM
Aperture

diam, arcsec
Aperture Area

arcsec^2
Aperture Integral

percent

Notes

Camera

Pixel Size

The fundamental width of the detector photo-site, assumed to be square. To calculate for a binned image, change the Binning field but do not change the fundamental Pixel Size. For example, suppose your CCD has a 9 micron pixel. To use a 2x2 binned image with effective 18 micron pixels, set Pixel Size=9 and Binning=2. All calculations are made for binned pixels.

Binning

The number of detector pixels per image pixel. This assumes the detector is binned n x n, where n = 1, 2, etc. See the Pixel Size parameter.

Readnoise

The detector readout noise is the intrinsic rms noise in a zero second exposure.

Gain

The number of electrons per ADU (Analog to Digital Unit) or DN (Digital Number) in the image.

Temp

The temperature of the detector.

T doubling

The doubling temperature for dark current approximated as a line in a log-log plot of dark current versus temperature. See the detector's data sheet.

Tref

The reference temperature for the detector Dark Current. See the detector's data sheet.

Dark Current

The rate of thermal electron production at a refernece temperature. See the detector's data sheet. The dark current is calculated using a simple doubling rule starting from a known reference dark current at a reference temperature. This is a very good approximation when the sensor temperature is not too far below the reference temperature, say within 5 or 6 doublings. However, getting even further below the reference temperature, the dark current can become so small that it has negligible effect on the calculated SNR.

Instrument

Focal Length

The telescope focal length in mm.

Diameter

The telescope primary diameter in mm.

Secondary

The telescope secondary obstruction in mm.

Efficiency

The percentage transmission of the optical system in the selected bandpass.

Bandpass

Name

The name corresponding to the filter set. This selects the photon flux for a star with the spectrum of Vega and magnitude 0 in the selected bandpass above the atmosphere.

Filter Factor

A response or transmission factor for the bandpass filter relative to the standard bandpass. This should usually be 100% unless using a low transmission filter.

QE

The quantum efficiency of the detector in the named bandpass. See the detector's data sheet.

Extinction

The atmospheric extinction coefficient in the named bandpass. This is site dependent. If set to 0.0, nominal values are adopted.

Airmass

The airmass, or optical path length through the atmosphere. The shortest path is through the zenith, which has the minimal airmass value of 1.0. The airmass of an observation is approximated by sec(z), which is the secant of the zenith angle. If set to 0, the observation is considered above the atmosphere.

Observations

Magnitude

The magnitude of the target star through the bandpass filter. This magnitude must be adjusted to the bandpass, e.g., use a V magnitude for the V bandpass, B magnitude for the B bandpass, etc.

Exp Time

The exposure time in seconds.

Seeing

The FWHM of the point spread function which is a product of the atmospheric smearing and optical abberations.

Sky Mag

The sky brightness per square arcsecond in the named bandpass. Sample values for a very dark site are around 21.8 to 22 in B and 21.3 to 21.5 in the V bandpass.

Computed Values

Aperture

This is the value of the measuring aperture radius that you would specify in Mira. Some software packages specify the aperture in terms of diameter, not radius. Be sure you enter the appropriate value. Enter a value using binned pixels that you see in the image. For example, setting Aperture = 9 at Binning=1 gives the same arcsecond radius as Aperture = 4.5 at Binning=2.

Aperture Integral

The fraction of the star's light inside the photometry aperture, assuming a circular Gaussian profile and a circular aperture.

Total BG Noise

The total noise in the background underneath the star. This includes readout noise, digitization noise, dark noise, and photon noise from the sky.

Sky / BG

The ratio of sky photon noise to total background noise (which includes sky noise). If this field is 1.0, then the sky photon noise is the only source of noise in the background underneath the star. This result helps you address the question of whether an observation is "sky limited" or "sensor limited".

Reference for equations and theory:

Newberry, M. V. 1991, PASP 103, 122-130.

 


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