Rescharts slanted-edge modules Part 4: Other results

Imatest Rescharts slanted-edge modules perform highly automated measurements of several key image quality factors using specially-designed test charts. The user never has to manually select Regions of Interest (ROIs).

This page covers results that are (mostly) not derived from the slanted-edges themselves, including

  • Noise (best in eSFR ISO)
  • Distortion  (differing detail in different modules; best with SFRplus and eSFR ISO. Described in detail here.
  • Tonal response*  (no noise statistics for SFRplus)
  • Color accuracy*  when used with an SFRplus, eSFR ISO, or SFRreg center charts that contain a color pattern
  • Vanishing resolution, aliasing, and Moiré from Wedge patterns in eSFR ISO
  • ISO sensitivity*  (Saturation-based and Standard Output Sensitivity) for charts with a grayscale pattern, when incident lux is entered
  • Image, Geometry, Distortion, Field of View  for all charts

*only for charts with tone and/or color patterns. Not in SFRreg (without center chart) or Checkerboard.

Edge-derived sharpness measurements and text (JSON and CSV) output files are covered in Part 3, which applies to all Rescharts slanted-edge modules.

Results – Tonal response and gamma – Image, Geometry, Distortion, FoV – Radial distortion – 
Summary and EXIF data – Color analysis – Detailed noise plot – Wedge aliasing & MTF – 
Multi-wedge plot – Summary – Links


This page combines results for the four Rescharts slanted-edge modules
that have automatic region detection,
 SFRplus, eSFR ISO, SFRreg, and Checkerboard. 
These modules contain many common results, making it
easier to maintain a single page than four separate pages.

In many cases we will use SFRplus as an example. Other module produce similar results.

New in Imatest 5.1  Chart MTF compensation has been added to compensate for chart limitations. This can double the maximum megapixel capacity of most charts.

Imatest 5.0  Nonuniform lighting perpendicular to the edge can be compensated. This improves the estimate of summary metrics such as MTF50.


Four introductory pages —  SFRplus, eSFR ISO, SFRreg, and Checkerboard — describe each module and explain how to obtain and photograph the chart.

Rescharts Instructions Part 2 shows how to run the modules inside Rescharts and save settings for automated runs.



When calculations are complete, results are displayed in the Rescharts window, which allows a number of displays to be selected. The following table shows the figure that displays specific results. Displays are numbered, but the numbers are different for different modules. Results from slanted-edge measurements are in Part 3.

SFRplus display selections

Slanted-edge Measurement  (Part 3) Display
MTF (sharpness) for individual regions Edge and MTF
MTF (sharpness) for entire image Multi-ROI summary
3D plot
Lens-style MTF plot
Lateral Chromatic Aberration Chromatic Aberration
Acutance/SQF (Subjective Quality Factor) Acutance / SQF
Edge roughness Edge roughness
Noise (from slanted-edges) Histograms and noise stats
Point Spread Function (approximate) PSF plot
Other measurement  (this page) Display
Image, Geometry, Distortion, Field of View Image & geometry
Distortion (geometric– radial plot) Radial Distortion Plot
Tonal response & gamma Tonal response & gamma
Detailed eSFR ISO noise Detailed noise plot See Multicharts/Multitest/eSFR ISO Noise 
Color accuracy a*b* Color error
Split colors
ISO Sensitivity Tonal response & gamma
Uniformity/Light falloff profiles Color & lightness uniformity profiles
EXIF data Summary & EXIF data
Wedge resolution, aliasing, & MTF
[eSFR ISO-only]
Wedge aliasing & MTF
Multi-wedge plot

Settings that affect each display will be shown. Most of these settings are not listed in Part 2. They are saved for Auto runs.

Tonal response and gamma display

eSFR ISO and SFRreg center chart

Results in Rescharts window: Tonal response, Gamma, White balance
from the circular grayscale pattern in eSFR ISO or the SFRreg center chart

For SFRplus this display is derived from the 4×5 stepchart pattern, located just below the center of the chart. It resembles the third figure in Stepchart. The upper plot shows the tonal response (also called OECF for Opto-Electronic Conversion Function) for all colors. The lower plot shows the white balance error (deviation from neutral gray) in the three ΔC units shown in the legend. The value of gamma may differ slightly from the values in the Edge response and MTF display because it’s calculated differently– based on the average slope of the light to middle tone squares of the stepchart. The levels of the light and dark portions of the patches used to calculate MTF are shown as pale horizontal lines and as points on the extreme left and right of the upper plot. You can use these lines to see if the patches are within the (relatively) linear region of tonal response (they are in the example on the right). A warning message (Warning: MTF patches may saturate) is displayed if any of the patches are close to saturation (log(pixel level/255) > -0.01; roughly, pixel level > 249 of 255).

Plot settings area

This area (lower-right of the Rescharts window, below Display) lets you choose which results to display. the contents of this section are different for each plot. Many of the selections are saved for Auto mode plots. The tonal response has only two settings: Channel (described in part 2) and Lower plot, which can one of the following.

Local Contrast the derivative of the density response: the local value of gamma
Delta-C ab, 94, 00 The indicated color difference (omitting luminance difference)
Delta-T The deviation of the correlated color temperature (degrees Kelvin) from neutral
Mireds micro-inverse degrees: a measure of color error used for calculating correction filters.


Image Stats opens the current image in the Image Statistics module, which allows portions of the image to be examined in detail. It provides cross-sections, historgrams, Fourier transforms, and more.


Distortion statistics, shown in the lower left, are described in detail in SFRplus Distortion and Field of View Measurements.

  • SMIA TV distortion is the simplest overall measure of distortion. it is positive for pincushion distortion and negative for barrel distortion.
  • k1 (the third order distortion coefficient). ru = rd + k1 rd3 = where ru is the undistorted radius and rd is the distorted radius. r is normalized to the center-to-corner distance. k1 > 0 for barrel distortion and k1 < 0 for pincushion.
  • h1 and h2 (fifth order distortion coefficients). ru = rd + h1 rd3 + h2 rd5 A relatively large value of h2 with a different sign from h1 may indicate “wave” or “moustache” distortion, where the predominant distortion goes from barrel to pincushion (or vice-versa) as radius increases.

Arctangent/tangent distortion coefficients (used in Picture Window Pro) are also calculated and included in the CSV output file.

Color & lightness uniformity profiles

Color & lightness uniformity profiles
Uniformity profiles


This display is similar in some respects to the profile plots in Light Falloff. It consists of profiles of the light areas (average values of rectangles between squares). Left-to-right profiles of the top, middle, and bottom of the image are shown on the left side of the display, and top-to-bottom profiles at the left, center, and right of the image are shown on the right. The following display options are available.

R, G, B, and Y unnormalized (max = 1)

R, G, B, and Y normalized (max = 1)

R, G, B, and Y unnormalized (max = 255)

R/G (Red) and B/G (Blue) unnormalized

R/G (Red) and B/G (Blue) normalized (max = 1)

Delta-L* (gray), a* (R), b* (B), chroma c* (G)

For best results with this display, you should make every effort to illuminate the target uniformly using techniques in The Imatest Test Lab. Brightness-related results (R, G, B, Y, and Delta-L*) cannot be measured as accurately as with Light Falloff, where the recommended technique calls for a clear uniform image field photographed through opal diffusing glass. But they can still be useful. The color ratios (R/G, etc.) can be especially useful for diagnosing uneven color response.

Image, Geometry, Distortion, FoV

All modules

SFRplus_results_imageImage, Geometry, Distortion, FoV display

This display allows several aspects of the image to be viewed in detail. It shows the selected regions for MTF/noise analysis (violet rectangles), the yellow rectangles used for generating the uniformity profiles in SFRplus, and the red horizontal curves used to measure distortion in SFRplus). Display options include

Original Image Extreme Lighten (HSL)
Rec channel Lighten (HSV)
Green channel Lighten 1 bit
Blue channel Lighten 2 bits
Color: Boost Sat. 4X Original w/5×5 grid
Color: Boost Sat, 10X Original w/5×7 grid
Lighten (HSL) Original w/11×15 grid

A number of geometrical results are shown beneath the image.

Distortion statistics are described in detail in SFRplus Distortion and Field of View Measurements. You can view the distortion-corrected image using a checkbox in the Display area on the lower-right of the Rescharts window.

  • WxH of image in pixels; m x n squares found; ROI size (referencing input setting), number of ROIs for MTF, etc. (not for profiles).
  • SMIA TV distortion is the simplest overall measure of distortion. it is positive for pincushion distortion and negative for barrel distortion.
  • Third order distortion coefficient k1.  ru = rd + k1 rd3 = where ru is the undistorted radius and rd is the distorted radius. r is normalized to the center-to-corner distance. k1 > 0 for barrel distortion and k1 < 0 for pincushion.
  • Fifth order distortion coefficients hand h2 . ru = rd + h1 rd3 + h2 rd5 A relatively large value of h2 with a different sign from h1 may indicate “wave” or “moustache” distortion, where the predominant distortion goes from barrel to pincushion (or vice-versa) as radius increases.
  • Arctangent/tangent distortion coefficients are also calculated and included in the CSV output file.
  • Field of View (FoV) is calculated from the selected distortion calculation or the best of three calculations (3rd,order, 5th order, arctan/tan, i.e., the calculation with the least optimizer error).
  • x,y coordinates of the center of the middle square relative to the image center.
  • The average rotation of the pattern in degrees (>0 for clockwise)
  • The bar-to-bar vertical height as a fraction of the image height and in pixels.
  • Convergence angles (degrees). These are the result of perspective distortion, when the camera is not pointed directly at the target or is misaligned. The horizontal convergence angle (related to yaw) is shown below: calculated by extrapolating the horizontal bars to the top and bottom. A positive angle has a vortex to the left. In the illustration below the pairs of solid red lines at the top and bottom are parallel (to fit the image on the page).

Horizontal convergence angle

Perfect alignment would be x,y coordinates, rotation, and H,V convergence = 0. Marks may be added to the top and bottom white space of the SFRplus image to facilitate alignment. Vertical convergence angle is derived from lines connecting the right sides of the left-most squares and the left sides of the right-most squares (shown as vertical blue dashed lines – – – above). With fisheye (strongly barrel-distorted) lenses the chart must be precisely centered for the convergence angle measurement to be meaningful.

  • measured focal length of the lens is displayed when Bar-to-bar chart height in cm, Lens-to-chart distance in cm, and Pixel spacing (pitch) have been been entered. It is written to the CSV output file if calculated. Equations: Magnification M is bar-to-bar height (on the sensor) / bar-to-bar height (on the chart). For Lens-to-chart distance f1, lens-to-sensor distance f2 = f1M. Using the thin lens equation, focal length f = 1/(1/ f1+1/ f2).
  • Field of view calculations include the effects of distortion (the best of 3 models is used). FoV in centimeters (cm) is displayed if the bar-to-bar vertical distance (in the chart center for pre-distorted charts) is entered. FoV in degrees is displayed if the lens-to-chart distance in cm is also entered.

A particularly interesting display is available when you click Crop to ROI (or Crop to 1/2 ROI). The ROI is displayed large enough so its blur is clearly visible and can be compared with Edge and MTF plots and summary results.

Image, Geometry, Distortion, FoV display, showing Crop to ROI, which allows
the edge appearance (enlarged) to be compared to Edge and MTF results.

Example: highly distorted Checkerboard image with lines and arrows

The relationship between the original and corrected image can be displayed (in Checkerboard-only) when Display arrows & lines is selected in the Display options area of the More settings window. The lines in the original image (below, left) give a good visual indication of how well the calculated coefficients correct the distortion. 

Distorted image with arrows: uncorrected and corrected. Click on image to view full-sized.
Original image Corrected image

The magnification for the corrected image can be adjusted a slider on the lower-left of the Rescharts display area.

Radial distortion plot

The radial distortion plot adds considerable detail to results in the Image, Geometry, Distortion, FoV display. This plot has four display options:  1. Delta-r, or 2. Lens Geometric Distortion (LGD)3. r undistorted (ru), or d(LGD)/d(ru). LGD is shown below.

SFRplus Radial Distortion plot showing Lens Geometric Distortion 100% ( rdru)/ru

The plot contains

  1. the change in radius Δr (normalized to the center-to-corner distance, i.e., the half-diagonal) as a function of the distorted (input) radius rd.
    Δr = r(undistorted) – r(distorted) = rdru
  2. Lens Geometric Distortion (LGD), which is included in the CPIQ Phase 2 specification, and is equivalent to Optical Distortion (defined by Edmund Optics).
    LGD = 100% ( rdru)/ru
  3. Undistorted radiusru 
  4. Curvature d(LGD)/d(ru). This curvature (new in Imatest 5.0) may be useful for determining the visual degradation caused by distortion, which is likely to be proportional to the maximum-minimum values. A change in sign may be a better indicator of mustache (wave) distortion than a change in 5th order polynomial sign (which isn’t always calculated).

The solid lines show results for correction formulas: ru = rd + k1 rd3 (3rd order; blue); ru = rd + h1 rd3 + h2 rd5 (5th order; green); or the arctan/tan equations (red). The best fit (5th order in this case) is shown in bold. With these equations |Δr| often increases as a function of r(distorted), i.e., it tends to be largest near the image corners. The selected value (or the one with the least error, err) is shown in boldface.

The radial plot is used to compare results from several Imatest distortion modules in Distortion: Methods and Modules.

Summary & EXIF data

All modules

This plot contains summary results for individual ROIs and EXIF data (metadata that describes camera and lens settings). When first installed, Imatest reads EXIF data from JPEG files only. Enhanced EXIF support requires a special download of ExifTool, described here.EXIF data may be viewed at any time from any display by clicking File, View All EXIF Data.

Summary results and EXIF data
Summary & EXIF data

Color analysis

eSFR ISO and SFRreg center chart

A color analysis is available for images that contain the optional SFRplus color pattern, which consists of 20 colors in 4 rows and 5 columns. 18 of the 20 colors are close to the colors of the industry-standard 24-patch color chart. The other two are on the yellow and blue sides of neutral gray. To obtain a color analysis,

  • The Color chart checkbox in the SFRplus Setup window must be checked.
  • The correct Color reference (file name) and Color space must be entered in the Settings region of the Settings window.

Two displays are available in the color analysis. The a*b* color error display, shown on the right, is similar to displays in Colorcheck and Multicharts. This display shows the reference (nominal) {a*,b*}values as squares and the camera (measured) values as circles. Normally the mean and maximum values of ΔE*ab, ΔC*ab, ΔE*94, ΔC*94, ΔE*00 and ΔC*00 are displayed.

SFRplus color chart

SFRplus chart with optional color pattern

The Split (Reference/Input) display is shown on the right. The bottom shows statistics for Row 2, Column 4, obtained by clicking Probe in the Display area on the lower right (not shown).

To turn off the probe, click outside the image (in the current version, you need to ckickon the text below the image. This should be fixed in a future version.) When the Probe is off the mean and maximum values of ΔE*ab, ΔC*ab, ΔE*94, ΔC*94, ΔE*00 and ΔC*00 are displayed.

a*b* color errora*b* color errorSplit color sidplay with probeSplit view, showing Probe results

Noise plot

eSFR ISO and SFRreg center chart

eSFR ISO can display several types of noise, measured from the grayscale patches surrounding the center of the chart, including all types of noise calculated by Multicharts and Multitest (standard pixel noise, chroma noise, scene-referenced noise, sensor (raw) noise, and ISO-15739 visual noise). SNR (Signal-to-Noise Ratio) can also be displayed as a ratio or in dB.

Instructions for selecting the noise display and x-axis and descriptions of the noise displays are on Multicharts/Multitest and eSFR ISO Noise.


The figure on the right— simple pixel noise, expressed as a percentage of the maximum pixel value— is one of the simpler noise displays.


Noise plot (for simple pixel noise)


Wedge MTF and Aliasing plot

eSFR ISO-only

If the Enhanced or Extended chart has been photographed and the Wedge checkbox in the eSFR ISO Setup window has been checked, the four wedge pairs are automatically detected, and one of two results for each pair (MTF and Aliasing onset, shown on the right, and Moiré) can be displayed. These plots are described in detail in the Wedge module page.


Wedge MTF and Aliasing onset plot
for Enhanced and Extended eSFR ISO charts
(a Moiré plot is also available.)


Multi-Wedge plot

eSFR ISO-only

The Multi-Wedge plot shows a summary of results for all wedges. It is the exact counterpart of the Multi-ROI (edge) summary plot for slanted-edges.

The multi-ROI (multiple Region of Interest) summary, shown in the Rescharts window (above), contains a summary of eSFR ISO wedge results. The upper left contains the image in muted gray tones, with the selected high frequency wedge regions surrounded by red rectangles and displayed with full contrast. The low frequency wedge regions, which are primarily for low frequency normalization, are inside blue rectangles. Up to four results boxes are displayed next to each region. The results can be selected in the the Display options area on the right, below the Display selection. There is a legend below the image.

Alias onset, MTF50, MTF20
Alias onset, MTF50, min(MTF10,alias,Nyq)
Alias onset, MTF50P, MTF20_
Alias onset, Secondary rdouts 1,2
All three secondary readouts

Results selection

View selection


  • The onset of aliasing is the frequency where the number of detected bars (smoothed to reduce sensitivity to noise) drops to 95% of the low frequency value. It is only indicative of aliasing on relatively sharp systems (good lenses in good focus, so there is some energy around the Nyquist frequency).
  • min(MTF10, alias, Nyq) (the minimum of MTF10, the onset of aliasing, and the Nyquist frequency (0.5C/P)) is the proposed ISO 16505 resolution metric (selected because MTF10 is not robust). See “Measuring MTF with wedges: Pitfalls and best practices” (presented at the Electronic Imaging 2017 conference).


  • SFRplus analyzes images of the SFRplus test chart, ideally framed so that there is white space above and below the horizontal bars in the chart, i.e., so neither bar runs off the top or bottom of the image. The white space should be between 0.5% and 25% of the image height. SFRplus can work without the bars, but distortion and field of view are not calculated. The bars may run off the sides of the image. Interfering patterns (bars, etc.) outside the chart should be kept to a minimum.
  • eSFR ISO should be framed to the registration marks are well inside the image. Where possible the entire chart should be inside the image. eSFR ISO has less spatial detail than SFRplus, but has wedges and larger tonal patches that allow much more detailed noise analysis.
  • SFRreg is highly flexible, and can include individual charts facing the camera with angular fields of view well over 180 degrees.
  • Checkerboard uses a simple checkerboard (chessboard) pattern that works over a wide range of distances: chart framing is not critical. 
  • Lighting should be even and glare-free. Lighting and alignment recommendations are given in The Imatest test lab.
  • The first time any of these modules is run, it should be run through Rescharts. This allows
    • parameters to be adjusted and saved for later use in the automatic version, which is opened with a (module) Auto  button in the Imatest main window.
    • results (listed above) to be examined interactively in the Rescharts window.
  • The Auto buttons in the left column of the main Imatest window runs the corresponding module in full automatic mode using settings saved from the most recent Rescharts run. Batches of files can be run.
Table of Rescharts slanted-edge MTF modules. (All also available as batch-capable fixed modules.)
All feature automatic region detection, ISO-compliant MTF (sharpness) analysis, and Lateral Chromatic Aberration calculation.
Feature   SFRplus
Sharpness map detail High Medium Depends on arrangement High
ISO-standard chart design
Color analysis *
Tonal response (OECF) *
Noise analysis Limited * Limited Limited
Distortion Limited
Geometry *
Features and
recommended uses
Imatest’s original automatically-detected chart, in use since 2009. robust and versatile. Some white space recommended above and below top and bottom bars. More spatial and distortion detail than eSFR ISO.
ISO-standard chart design. Includes wedge analysis. Supports detailed noise analysis.

Several individual charts are typically placed around the image field. Works with
-extreme fisheye lenses (>180º)
-the Optikos Meridian system.
-Charts at different distances to test focus & depth of field.
-extreme high resolution cameras (>36MP)

*Available with SFRreg center chart in Imatest 5.0+. FoV is omitted from geometry.

Relatively insensitive to framing: can zoom in or out as long as distance is large enough so chart quality is not an issue and there are detectable corners.

♦ denotes strong support;  – denotes no support.