Star Chart

 Analyze the Siemens Star chart

New in Imatest 2020.1 (Feb. 2020)  Shannon information capacity can be calculated from images of the Siemens star, with much better accuracy than slanted-edges. The old slanted-edge method has been deprecated.   The white paper, “Camera information capacity: a key performance indicator for Machine Vision and Artificial Intelligence systems“, which briefly introduces information theory, describes the camera information capacity measurement, then shows results (including the effects of artifacts) is now available for download. Imatest 5.0: Half-stars (rotated by multiples of 45º) can now be analyzed. A star-only pattern (without density patches, etc.) can be selected in Chart configuration. Stars with no inner circles can be analyzed. Bar (square wave) star patterns can be analyzed with a few restrictions. Stars with 24 or 16 cycles can be analyzed. Imatest 4.0:  Automatic region detection is available for a new version of the Star Chart that has registration marks on the sides. See below. A new web page, Slanted-edge versus Siemens Star – A comparison of sensitivity to signal processing, has been published.

Photographing the chart and running the program

Star Chart measures MTF from a star pattern along the radii of a circle for a range of angles (in 8, 16, or 24 segments). Although sinusoidally-modulated patterns are preferred, bar (square wave-modulated) patterns will work with an appropriate normalization setting. This method is more direct than the slanted-edge method, but requires more real estate. Because calculations are performed on circles of known spatial frequencies, the results are more robust against noise than Log Frequency, which also uses a sinusoidally-modulated pattern.

Image with star chart (upper right)

The image above was used to compare Star chart results with Slanted-edge SFR and Log Frequency. It was captured with a Canon EOS-40D camera, 24-70mm f/2.8L lens set at 50mm, f/5.6, ISO 100. It includes Star, Log Frequency-Contrast and slanted-edge charts with high and low contrast (20:1 and 2:1).

We recommend that you purchase test charts from the Imatest Store. You can also create a file with the Imatest Test Charts module that can be printed on a photographic quality inkjet printer. Recommended options are PPI: 720 (Epson inkjets) or 600 (HP or Canon inkjets), Height (cm) (as required), Highlight color: White, Contrast ratio: 50, Type: Sine, Gamma: 2.2, Star pattern bands: 144 or 72 (for high or low resolution cameras, respectively), Chart lightness: Lightest, ISO standard chart: Small (1/20) inner circle (inner circle has 1/20 the diameter of the outer circle). Cheap bond paper and laser printers are strongly discouraged.

Number of chart cycles   Ideally the maximum spatial frequency (just outside the inner circle) should be around 0.6 to 1.0 cycles/pixel. The diameter of the inner circle di is typically 1/20 times the diameter dP of the circular star pattern, depending on the chart (selectable in Test Charts). The smallest diameter for analysis is 0.056dP or near-zero (for no center circle). For an image of P pixels (width or height) of a star with N cycles, where the pattern circle diameter dP takes up a fraction g of P (dP = gP;  di = 0.056 gP ) , the maximum spatial frequency in cycles/pixel is \( f_{max} = \frac{N}{0.056 \pi d_{P}} = \frac{N}{0.056 \pi g P}\)      (inner circle 1/20 the diameter of the outer) Example: for a 3000 pixel wide image where the pattern circle dP takes up g = 1/3 (33.33%) of the image and the inner circle has 1/20 the outer diameter,  fmax = 0.818 cycles/pixel for a 144-cycle pattern;  fmax = 0.414 cycles/pixel for a 72-cycle pattern. The 144-cycle pattern is indicated. 72-cycle patterns are most suitable for low resolution cameras (~2 megapixels or less).

Mount the chart on a flat dark board— 1/2 inch foam board works well; thinner board warps more easily. Depending on the number of horizontal pixels in the image to be analyzed, the chart should occupy approximately 500-2000 pixels, typically 1/3 to 1/4 of the horizontal frame for high resolution cameras (more of the frame for lower resolution cameras: VGA, etc.). Other charts can be mounted along with it.

Orientation. 

The chart itself contains no clear indication of the recommended orientation. We recommend the following orientation (though Imatest will correct for incorrectly oriented charts).
– The pattern should be oriented horizontally, i.e., in landscape orientation (it is slightly wider than high).
– The darkest grayscale patches should be in the lower-right of the image; the lightest should be in the upper-right.

Photograph the chart using glare-free even lighting (±5%, which should be easy to achieve since the chart is relatively small), as described in Building a Low-Cost Test Lab or How to test lenses. Save the image in any one of several high quality formats, but beware of JPEGs with high compression (low quality), unless you are testing for JPEG degradation.

Because resolution varies over the image for most cameras and lenses, the chart should not take up too much of the frame.  The active chart height (the Star diameter) should be between about 500 and 2000 pixels, with at least 800 pixels recommended for high resolution cameras. For typical high resolution cameras the active chart height should be no more than about 1/3 to 1/2 of the total image height, i.e., the area of the star pattern should not exceed about 1/8 of the total chart area. This recommendation does not apply to low resolution systems such as VGA, which need at least 300 pixels of active chart height (more if possible). Here is additional information from the page on Shannon Information Capacity. The size of the star in the image should be set so the maximum spatial frequency, corresponding to the minimum radius rmin, is larger than the Nyquist frequency fNyq, and, if possible, no larger than 1.3 fNyq, so sufficient lower frequencies are available for the channel capacity calculation. This means that a 144-cycle star with a 1/20 inner marker should have a diameter of 1400-1750 pixels and a 72-cycle star should have a diameter of 700-875 pixels. For high-quality inkjet printers, the physical diameter of the star should be at least 9 (preferably 12) inches (23 to 30 cm). Other features may surround the chart, but the average background should be close to neutral gray (18% reflectance) to ensure a good exposure (it is OK to apply exposure compensation if needed). The figure on the right shows a typical star image in a 24-megapixel (4000×6000 pixel) camera.

Open Imatest, then click on Rescharts to run from the interactive Rescharts window or Star to run as a fixed module.

In Rescharts the Chart configuration dropdown menu can be used to select the chart type. It should be set prior to reading the image. Three settings are available (as of Imatest 5.0). Star (black squares in corners) is the traditional design with density patches around the star and white squares inside larger black squares at the corners. Star (registration marks on extended sides), shown on the right, is a newer design that includes registration marks and slanted-edges on the sides. It works with Automatic ROI detection (selected in the ROI Options window). Star-only omits all extra graphics. Just the star and nothing more.

In Rescharts, select the pattern to analyze (in this case, Star Chart ) by clicking on the appropriate entry in the popup menu below Read image file or by clicking on Read image file if Star Chart is displayed. The Read image file button and popup menu (shown on the right) are highlighted (yellow background) when Rescharts starts.

Select the image to read. If the pixel size is the same as the previous Star Chart run, you’ll be asked if you want to use the previous ROI, adjust the previous ROI, or crop anew. If the folder contains meaningless camera-generated file names such as IMG_3734.jpg, IMG_3735.jpg, etc., you can change them to meaningful names that include focal length, aperture, etc., with the Rename Files utility, which takes advantage of EXIF data stored in each file.

Cropping  The initial crop should include the entire pattern, including the outside of the black rectangles (with the small white squares inside). It doesn’t have to be precise because it will be refined in the ROI fine adjustment window, shown below. The ROI fine adjustment window may be maximized to facilitate fine selection.

In the ROI fine adjustment window the pattern should be cropped so

• the middle cyan square is at the bounds of the large star pattern circle (or slightly inside if there is distortion),
• the inner cyan square is on the inner circle (which consists of four quadrants— two white, two black) for inner circles with 1/10 the diameter of the outer. (The inner circle will be well inside of the inner cyan square for small inner circles, which have 1/20 the diameter.),
• the magenta crosshair inside the inner circle is well-centered. If it is slightly off Imatest will automatically correct it.

ROI fine adjustment window showing the cropped Star Chart image
Canon EOS-40D camera, 24-70mm f/2.8L lens set at 50mm, f/5.6, ISO 100.
Click here or on the image to load full-size test image.

Distorted images The image on the right has significant keystone distortion. For such cases (including optical distortion – barrel or pincushion), make sure all the outer borders are inside the star and, most importantly, make sure the selected region is centered close to the center marker (indicated by the cyan square and magenta cross patterns), as shown below.Centering doesn’t have to be perfect because the program will perform a final centering operation prior to the calculations. But it has to be close for this operation to work properly.

 

If Express mode is not selected, the input dialog box shown below appears. In Rescharts this dialog box can be at opened any time by pressing the More settings… button.

Settings

There is no setting for the number of chart cycles because it is automatically detected.

Chart configuration applies to the next run. You can choose between the traditional design, which has no registration marks, or newer designs that work with automatic ROI detection. It can also be selected from the Chart configuration dropdown menu in Rescharts.

Normalization selects the MTF normalization method (where to set MTF to 1.0):

1. normalize to the outer MTF value for each segment (the default),
2. normalize to the maximum outer MTF value in all segments, or
3. normalize to the difference between the lightest and darkest of the grayscale square patches near the pattern edge. This often gives the best estimate. Does not work with bar (square wave) charts.
4. Normalize by extrapolating smoothed MTF to 1 at f = 0 (OK for simple curves)

(1) may be slightly better when illumination is nonuniform. (2) may be slightly better when actual MTF varies between segments. (3) is usually better because the lowest spatial frequencies in the star may not be low enough approximate zero spatial frequency.

Bar (square wave-modulated) star patterns are analyzed similarly to sine patterns (which are usually recommended), but the correct normalization is required because the fundamental sine component of a bar pattern (square wave) is 4/π times the bar pattern amplitude. Normalization settings 1, 2, or 4 (but not 3 – Normalize to darkest-lightest outer square) work with bar star charts.

 

Inner circle  May have 1/10, 1/20 the diameter of the outer circle or may be omitted (No inner circle). Should match the chart. Affects the maximum spatial frequency of the analysis. The inner circle consists of a registration mark (quadrant pattern), which is used to refine the region alignment. If it is omitted, you must be extremely careful to center the pattern (using a + indicator) when making the ROI fine adjustment.

Star type  FULL (default) or Half-auto.

FULL assumes a full star with segment 1 centered at 0º.

Half-auto assumes a half or full star, automatically detected, but centers segments differently to correspond to the star orientation, so the first and last edges are located at multiples of 45º. Half-stars are a feature of the TE42 test chart, which will be supported by the Imatest Arbitrary charts module.

Calc segments is the number of segments around the circle to display in the analysis. Select 8 (the default; recommended for most work), 16, or 24. (16, which works better with half-stars, replaced 12 in Imatest 5.0.) Calc. segments should never be more than half the number of chart cycles. 8 is the best choice most of the time.

Calc. radii is the number of radii on the circle used for the MTF calculations. 64 is slightly more accurate than 32, but somewhat slower (it’s the default for now). 128 is slower, contains more frequencies than needed, and is more susceptible to noise. It is no longer recommended (and may be deprecated).

Enter or calculate gamma  Choose between Calculate gamma & linearize from chart patches or Enter gamma for linearization. If Calculate gamma… is selected, the 16 small square patches at the periphery of the star chart are used to determine the value of gamma for linearizing the chart, Gamma (below) is disabled, and the displayed value of gamma includes the indicator (chart).

Gamma is used to linearize the test chart when Enter gamma… (above) is selected. It can be measured by Stepchart, Colorcheck, or Multicharts. 0.5 is a typical value for color spaces intended for display at gamma = 2 2 (sRGB, Adobe RGB, etc.). If gamma is entered (rather than calculated), the displayed value of gamma includes the indicator (input).

Channel is R, G, B, or Y (luminance; the default).

Calculate information capacity  turns on the Shannon information capacity calculation (Imatest 2020.1+).

Display options

MTF units, etc. selects the x-axis units. If Cycles/inch or Cycles/mm are selected, the pixel spacing (um/pixel, pixels/inch, or pixels/mm) should be entered.

Maximum x-axis frequency for linear plots selects the maximum spatial frequency to be displayed in linear plots. Star chart is the only module other than the slanted-edge modules that can analyze MTF above the Nyquist frequency (0.5 cycles/pixel).

Secondary readout  allows up to two secondary readouts (MTFnn, MTFnnP, or MTF at a specified spatial frequency) to be displayed on the MTF plots. Details here.

If you’re running from Rescharts, don’t worry about getting all settings correct: You can always open this dialog box by clicking on More settings….

After you press OK, calculations are performed and the most recently-selected display appears.