In high-precision photometry, the selection of the aperture radius is a pivotal step that directly influences the quality of your light curves. An aperture that is too small will miss flux in the outer parts of a star’s profile, while an aperture that is too large will encompass unnecessary sky noise and possibly flux from nearby sources. 


To assist the user in determining the optimal aperture radius for subsequent photometric measurements, Phoranso introduces the Optimal Star aperture finder. This tool supports both a Manual and an AI assisted workflow. The Manual mode is intended for in-depth analysis of individual stars, while the AI assisted mode performs a rapid, field-wide optimization. The tool eliminates guesswork in defining aperture ringsets by identifying the "sweet spot" where stellar flux is maximized while the contribution of background sky noise is minimized.



Manual mode 


Manual mode is ideal when you have a specific primary target and want to ensure its photometry is as precise as possible.  


  • Open a FITS file. We strongly recommend setting the zoom to 200%.

  • From the Tools menu, select Optimal Star aperture finder, then choose Manual mode

  • This opens an initially empty Optimal star aperture finder window:



  • Next use the mouse to select a star in your FITS image by clicking near its center. This will typically be your Target star, or one of your Reference, Check or Comparison stars, but any star in the image may be selected. Upon selection, the Optimal Star aperture finder window is populated with the analysis results.



Optimal Star aperture finder - Manual mode






By selecting a star, Phoranso generates a comprehensive diagnostic suite consisting of three synchronized plots. The three plots should be interpreted together to make an informed aperture choice. 



  1. Signal-to-Noise Ratio  

    This is the primary decision-making graph. It plots the Signal-To-Noise (SNR) of the selected star against a range of aperture radii in pixels. The curve typically rises steeply, reaches a maximum, and then gradually declines as more background noise is included. 

    Phoranso determines the Optimal Radius (in pixels) by fitting a smoothed SNR curve through all computed data points, and identifying the radius at which this smoothed curve reaches its maximum. This maximum is marked by a fixed cursor (drawn in purple), which automatically jumps to the peak representing the aperture radius that yields the highest expected data quality. Use the mouse scroll wheel to zoom in and out on the graph.

    In the illustrated example, the Optimal radius is 3.8 pixels.


  2. Curve of Growth 

    This graph plots the cumulative normalized flux of the selected star against the same range of aperture radii. It shows how the total captured stellar flux increases as the aperture radius is expanded.

    At small radii, only the central part of the star's point spread function (PSF) is enclosed. As the radius increases, more stellar flux is included and the curve rises steeply. Eventually, the curve flattens as most of the star's flux has been captured, and further increases in radius add mostly background noise rather than stellar signal.

    The tool computes the sum of all pixel values (minus the background) within each radius.  Phoranso color-codes this plot into three distinct regions:

    • Undersized zone (orange): the aperture is too small and significant stellar flux is lost. Apertures in this zone should be avoided, as photometry here is dominated by flux losses.

    • Target zone (green): The ideal region where the flux begins to level off. The Optimal radius identified from the Signal-to-Noise Ratio curve is usually located within this zone. If it is not, this may indicate that the selected star is affected by artefacts such as nearby sources or saturation.

    • Noise zone (yellow): in this zone, the flux increases only marginally, and background noise begins to dominate. Apertures in this zone reduce photometric precision and should generally be avoided unless special circumstances require very large apertures.

    Phoranso uses mathematical criteria to determine the boundaries between these three zones.


  1. Star Profile 

    This plot displays the radial intensity profile (Mean ADU) of the selected star over the selected range of radii. It represents how the mean pixel intensity decreases with increasing distance from the star's centroid, and provides direct insight into the star's point spread function (PSF), atmospheric seeing, and image focus.

    The radial intensity is computed over concentric annuli around the star center, and expressed in mean ADU. A well-focused, isolated star typically exhibits a steep central peak corresponding to the star core, a smoothly decreasing wing caused by atmospheric seeing, optical aberrations and detector respones, and a gradual transition into the background noise floor at larger radii.

    Phoranso fits a Moffat profile - a mathematically robust model for stellar PSFs (Point Spread Functions) - to the measured data. From this fit, the FWHM is determined and displayed as a fixed cursor. The Optimal aperture radius derived from the Signal-to-Noise Ratio curve is also shown. Finally we display the relation between Optimal aperture radius and the FWHM. In the illustrated example, the Optimal SNR radius corresponds to 2.3 x the FWHM.

    As a general guideline, optimal aperture radii typically lie between 1.5 x and 2.5 x the FWHM, although the exact value may depend on multiple factors. 


Once you have identified the optimal radius, enter the value into the Aperture photometry ringset field in the Photometry settings window.



At the top of the Optimal Star aperture finder, three additional fields are displayed:


  • Aperture radius range: allows to specify the aperture radius range, in pixels. This range defines the x-axis of all three plots.
  • Selected star centroid: displays the precise X and Y coordinates of the centroid of the selected star
  • A cut-out of the selected star: displays the selected star together with the calculated Optimal radius (in red). This allows visual inspection to verify whether the suggested optimal radius appears realistic. The cut-out uses the same zoom factor, orientation, and color scheme as the main FITS image.




AI assisted mode 


While Manual mode provides a surgical look at a single star, the AI assisted Star aperture finder leverages intelligent automation to evaluate the entire image frame. This mode is powered by an inference engine that attempts to emulate the cognitive workflow of a photometrist:


  1. Dynamic source validation: rather than simple tresholding, the engine performs a deep scan of the FITS frame to differentiate viable point sources from transients and noise. By evaluating the morphological characteristics of each candidate, the engine ensures that only physically significant stars enter the aperture optimization loop.

  2. Magnitude categorization: detected sources are autonomously partitioned into distinct populations -Faint, Moderate, and Bright stars - using an unsupervised clustering algorithm. This step evaluates the non-linear interaction between stellar flux, local background variance, and the Point Spread Function (PSF), unique to the current image frame.

  3. Intelligent sample filtering: the engine autonomously prunes the dataset, rejecting stars impacted by crowding, edge effects, or local artifacts. This ensures the recommended apertures are derived from statistically "clean" representative samples.

  4. Optimized aperture synthesis: in the final phase, the finder synthesizes the ideal aperture radii for each magnitude tier. By iteratively minimizing the noise contribution while maximizing flux integration, the engine provides an optimized aperture set that ensures photometric precision across the entire dynamic range of the FITS image.


Proposed workflow:


  • Open a FITS file. We strongly recommend setting the zoom to 200%.

  • From the Tools menu, select Optimal Star aperture finder, then choose AI assisted mode

  • An initially empty AI assisted Star aperture finder window is opened, and calculations start automatically. The progress of the AI engine is reported in the small dark green status bar at the bottom of the window.



  • Once the analysis is complete, the AI assisted mode presents its conclusions visually to maintain transparency: a representative star cut-out is displayed for each brightness class, a red aperture overlay indicates the AI-selected optimal radius (in pixels) for that class, the maximum SNR value associated with each class is displayed, as well as the X and Y coordinates of a representative star.



  • In the final step, select the brightness class that best represents your Target, Reference, Check or Comparison stars. Enter the corresponding Optimal radius value into the Aperture photometry ringset field in the Photometry settings window.  

    In the illustrated example, if your Target star is a faint object, you may choose to use an aperture radius of 2.5 pixels for the Aperture photometry ringset.


Notes on AI assistance


This is an AI assisted mode. Its performance and accuracy have been evaluated on hundreds of widely varying FITS images, and in the vast majority of cases, it produces aperture recommendations that are physically meaningful. As with any automated method, occasional outliers are possible. Users are therefore encouraged to visually inspect the results and, when necessary, refine the aperture choice using Manual mode.




Theoretical considerations


In an idealized situation, all stars in a single FITS image would share the same maximum SNR radius, meaning that their SNR curves would peak at the same aperture radius. This requires uniform background noise, linear and spatially invariant detector characteristics, and stars that are isolated and unsaturated. In this case, SNR curves differ only by a vertical scaling factor, with brighter stars achieving higher SNR at all radii.


In real data, several effects break this ideal behavior, including:


  • PSF variations across the field
  • Background variations (spatial gradients, vignetting, ...)
  • Different dominant noise sources (in bright stars the photon noise dominates causing the SNR peak to occur at slightly larger radii, while in faint stars the background noise dominates and SNR peaks shift to smaller radii)
  • Sensor saturation and non-linearity  
  • Image sampling effects
  • etc



Similarly, in an idealized image, all stars would share the same FWHM, since it reflects the global point spread function (PSF) of the optical system and the atmosphere at the time of exposure. In practice, FWHM almost always varies across an image due to optical field effects, imperfect field flattening, focus variations, sensor tilt, atmospheric seeing and related factors.