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Create Synthetic Image The Create Synthetic Image command creates realistic images containing noise and optionally, stars. These images are essential for evaluating processing and measurement algorithms and exploring the effects of noise and noise propagation through calibration strategies. The noise model used for creating the synthetic image includes all forms of noise. Optionally, a realistic distribution of randomly placed stars may be added with a Moffat or Gaussian point spread function ("PSF"). All Properties are specified in commonly used units of electrons (e-) and DN (or ADU's).
Theoretical BasisSchematically, the image value at any pixel location is given as follows:
where the Noise value is a Gaussian random value and may be positive or negative relative to the Background Value. The PSF is the sum of all overlapping Point Spread Functions at the given pixel location. All quantities use fundamental units of electrons (or photons) which are converted to pixel value in units of DN (Digital numbers, or ADU) as would be recorded in an image. As per convention in the field of scientific imaging, some Properties are entered using fundamental units while others are entered using ADU (or DN) units; the units are indicated on the Create Synthetic Image dialog. The Noise value above is computed from all sources of which all are assumed to be uncorrelated. The noise can be described as follows:
Notice that some of the noise terms are a function of the signal while others are constant. Of those that depend on the signal, Background noise is the "shot noise" of the background signal and PSF shot noise is the photon noise for all PSF's that overlap a given pixel location. All noise sources are computed in fundamental units of electrons (or, equivalently, photons). Example and Analysis of the Synthetic DataThe following example illustrates the process of creating and analyzing a synthetic star field. The image below shows a portion of the synthetic image produced using the Properties shown in the dialog above. This example created 10,000 artificial stars, most of which are faint because of the stellar luminosity function.
Data for the 10,000 artificial stars were listed in the Report window shown below. The listed intensity is not the peak value but, rather, gives the total volume under the Point Spread Function ("PSF"). This intensity is the target value for which the PSF was created, and hence it is a "pre noise" value. The actual intensity measured for any artificial star will differ because of random noise sources included in the model.
The Report window includes a pop-up menu which is opened by right-clicking the mouse, as shown below. After selecting (highlighting) the target star, the Go to Object command was clicked to center the image cursor on star 9889 as shown in the Report (note: this is different from the Go to Object command in the Coordinates menu). The centered star is shown in the image window below.
In the next picture, the Create Plot from Grid command was selected from the menu. If the positions of the artificial stars are random, then there should be no correlation between x and y coordinates. To investigate this, the scatter plot below was created from the tabular star data. After the plot was created, the Plot Series Properties command was used to change the default squares to smaller dots:
The following window shows a radial profile plot for one a medium-bright artificial stars. The calculated FWHM is 2.519, identical within the noise to the target FWHM value of 2.5. Remember that noise in the synthetic image results in measured quantities scattering about their known target value.
Another test shows the histogram of a region of "sky" background. The image region outlined below was sampled to produce the histogram plot following.
As shown below, the longer positive tail in the histogram results from the many, extremely faint stars present inside the sampling rectangle. Note that the sky histogram shows a Gaussian distribution because of the Gaussian random noise in the model and is centered on 1000 as specified in the parameter dialog.
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