# Chart Quality Calculator

Imatest 5.1 has several new features that let you use measured chart MTF (modulation transfer function) to

• determine the megapixel suitability of a test chart characterized by size, print media, and printing technology, as well as its suitability for a camera system characterized by sensor and pixel size, i.e., pixel count. This can help determine the appropriate test chart for a specific application.
• increase the accuracy of MTF measurements by dividing the measured camera MTF by the appropriately-scaled chart MTF, which is equivalent to deconvolution in spatial domain. This technique is described in Compensating camera MTF measurements for chart and sensor MTF. It improves the absolute accuracy and consistency of camera MTF measurements with a variety of test charts. It also lets you view the precise effect of chart MTF on camera MTF measurements.

The Chart Quality Calculator, introduced on this page, lets you estimate the effect of chart MTF on camera MTF measurements for a wide range of

• chart media and printing technologies (inkjet on reflective and transmissive media, photographic film and prints, etc.),
• cameras, characterized by sensor and pixel size (and hence pixel count),
• vertical fields of view (often related to chart size).

The Chart Quality Calculator lets you determine how large a chart (for media characterized by Chart MTF in cycles/object mm) is needed for a camera with a given number of megapixels, with or without chart MTF compensation. You don’t need chart images to use it.

Using it correctly requires a clear understanding of key concepts.

 Quick summary of the Chart Quality Calculator.  Details below. Open the Chart Quality calculator Read the MTF chart compensation file (contains coefficients of a chart MTF model calculated from chart measurements). Compensation files can be downloaded from www.imatest.com/docs/mtf-compensation/#compfiles . Enter the Vertical field in mm to calculate the Megapixel suitability table (displayed in the lower part of the window). Enter at least two of the following three parameters: (1) Camera pixel pitch in microns/pixel, (2) Magnification, (3) Sensor height in mm to obtain detailed results for a specific system. Several results will be displayed. The most important is MTF @ Nyquist frequency (fNyq = 0.5 cycles/pixel). If if is above 0.9, the chart is adequate without compensation. It it’s between 0.5 and 0.9, chart compensation is recommended. We don’t recommend charts with MTF @ fNyq < 0.5.

### Chart MTF

Chart MTF is measured using printed slanted-edges of reasonable contrast (between 4:1 and 10:1) with the measurement technique described in the Appendix (below). The spatial frequency unit for the chart MTF measurement is cycles/object mm, i.e., cycles per millimeter on the chart (not on the sensor, as is typical of most Imatest measurements). Here are a few details about the measurement (more in the Appendix, below).

• Magnification should be large enough (typically 1x or greater) so that the measurement is dominated by the chart quality, not by the lens, sensor, or signal processing. (Typical camera MTF measurements have magnifications of < 0.1 for high quality film charts and < 0.02 for inkjet charts.) Magnification should be carefully measured and recorded.
• The measured chart MTF is fit to a function that closely approximates actual response curves at frequencies where MTF > 0.3 (below MTF30). This function removes irregularities in the MTF curve caused by noise (typically at frequencies above MTF30) and facilitates further processing. The function is

$$\displaystyle MTF_{chart}(f) = e^{-a_1 f – (a_2 f)^2}$$ ;         f in units of Cycles/Object mm (C/Obj mm).

This function matches a wide range of observed chart MTF measurements.

#### Projected Chart MTF

When the chart is projected (imaged) on the sensor its spatial frequency units must be transformed to the native units of the sensor, Cycles/Pixel (C/P), by substituting,

$$f(\text{C/Obj mm}) = f(C/P) \times \text{magnification} \times \text{pixels/mm}$$

$$MTF_{chart-projected} (f) = MTF_{chart}(f(C/P) \times \text{magnification} \times \text{pixels/mm}) = MTF_{div}(f)$$

In Imatest sharpness modules, pixels/mm is typically derived from the user-entered value of pixel pitch (in μm), where pixels/mm = 1000 / (pixel pitch (μm)). Magnification is either entered in the settings window or derived from geometrical factors (like the bar-to-bar spacing in SFRplus or the vertical registration mark spacing in eSFR ISO).

If MTFdiv(fNyq) (MTFdiv at the Nyquist frequency (fNyq = 0.5 C/P)) is lower than 0.9 (90%), measurement accuracy can be improved by dividing the measured MTF by MTFdiv, as described in Compensating camera MTF measurements for chart and sensor MTF. If MTFdiv(fNyq) is greater than 0.9, there is little improvement.

#### The Chart Quality Calculator

The Chart Quality Calculator is opened from the Utilities dropdown menu in the Imatest main window. It lets you read in a chart quality (MTF compensation) file, which contains the measured coefficients for a specific media and print technique, and then select parameters that determine

• the Megapixel suitability (the largest number of camera Megapixels) that can achieve a given quality level for a chart of a specified size, and
• how chart quality affects MTF measurements for a specific system, defined by parameters that  include pixel pitch in microns (μm) per pixel, magnification, sensor height, and Vertical Field of View (which is closely related to chart height). When one of these parameters changes, one or more of the others is changed for consistency, according to rules in the following table.
Key chart quality settings that affect results (chart Megapixel suitability)
Setting Changes Affects  Description
Vertical field mm. magnification Megapixel suitability
MTF div plot
Vertical Field of View (FoV) is closely related to chart height, especially for charts designed to fill the Field of View (SFRplus, eSFR ISO, etc.). This is the only one of the four input settings that affects the Megapixel suitability table.
[magnification = sensor height/Vertical FoV]
um per pixel none of the other input settings MTF div plot and MTFnn Pixel pitch, usually entered as microns (μm) per pixel. Converted to pixels/mm in the above equations.
magnification sensor height mm MTF div plot Magnification must be measured carefully when an image is taken. For some modules (SFRplus, eSFR ISO, Checkerboard) it can be derived from geometrical chart features. [Sensor height = magnification * Vertical FoV]
Sensor height mm. magnification MTF div plot Sensor height in mm. [magnification = sensor height/Vertical FoV]
 Notes: MTFnn is the spatial frequency in Cycles/Pixel (on the image sensor) where MTF drops to nn% of the low frequency value Typical values of interest are MTFnn = 90, 70, 50, and 30.  Megapixel suitability is the maximum camera megapixels that the chart can reach at the specified quality level (MTF at the Nyquist frequency), typically for either a 4:3 or 3:2 aspect ratio. It is a function of the MTF chart compensation file (which can be downloaded from  www.imatest.com/docs/mtf-compensation/#compfiles .) and Vertical field in mm. (It’s not affected by the other inputs.)

Chart Quality Calculator window
Settings for a 5×7 Multi-size Color LVT SFRplus chart where the largest chart image has
a bar-to-bar spacing of 128mm, corresponding to a vertical FoV of 140mm = 5.51″.

### Key results

#### General megapixel suitability

These results, which are in the table titled  Megapixel suitability  near the bottom of the window, indicate

• the maximum number of vertical pixels and total megapixels that can achieve a specific quality level (derived from MTF at the Nyquist frequency) for a chart with the selected medium and vertical field of view.
• how large a chart needs to be to achieve a specified quality level for a camera with a known number of vertical pixels.

Neither of these results are affected by entries for pixel size (μm per pixel), magnification, or sensor height.

Megapixel suitability table for four quality levels at a specific vertical field height.

The table displays a number of results based on MTF at the Nqyuist frequency (MTF @ fNyq).  Measurements (maximum vertical pixels and camera Megapixel sizes for three aspect ratios (4:3, 3:2, and 16:9) and Quality levels (MTF @ fNyq = 90, 77, 70, and 50) are described in the two tables below. MTF @ Nyquist = 0.77 is a special case, approximating the MTF suitability calculation used prior to 2018. This number has proven to be a reasonably conservative estimate of MTF suitability without chart compensation.

MTF @  fNyq determines the effect of chat quality on MTF measurements and whether chart compensation is needed.

 Measurement Description Quality High, (Old Mpxl limit), Moderate, Minimum. There correspond to a minimum MTF at the Nyquist frequency (fNyq) for image of the chart on the sensor. MTF @ Nyq The minimum value of MTF @ fNyq for the image of the chart on the sensor. corresponding to the indicated quality levels:  0.9, 0.77, 0.7, and 0.5. Vertical pixels The maximum number of vertical pixels that can achieve the indicated quality level (MTF @ fNyq). This is the same number as the older Chart Quality Index. V-pxls/cm The maximum number of vertical pixels per centimeter of chart height that can achieve the indicated quality level. For a camera with n vertical pixels, the minimum chart size in cm is n/(V-pxls/cm) for the quality level indicated by the row. V-pixels/cm = 20*MTFnn(cycles/object mm) = 2*MTFnn(cycles/object cm)  (for nn = 90, 70, 50, etc.). Mpxls @ 4:3 The number of megapixels corresponding to Vertical pixels (above) for a 4:3 aspect ratio. Mpxls @ 3:2 The number of megapixels corresponding to Vertical pixels (above) for a 3:2 aspect ratio. Mpxls @ 16:9 The number of megapixels corresponding to Vertical pixels (above) for a 16:9 aspect ratio. um/pixel min The minimum pixel size (in microns) that can achieve the indicated quality level (MTF @ fNyq). Key results are shown with a yellow background.
 MTF @ fNyq Quality Description CQI MTFNyq ≥ 0.90 Excellent Chart compensation is not needed. CQI90 0.70 ≤ MTFNyq < 0.90 Good Chart compensation is optional but improves accuracy. CQI70 0.50 ≤ MTFNyq < 0.70 Comp. required Chart compensation is required for accurate results. CQI50 0.30 ≤ MTFNyq < 0.50 Minimal Will work with chart compensation, but this is stretching things.  Not recommended. MTFNyq < 0.30 Fail Don’t even think of it!  MTF is too low for reliable results (it’s too sensitive to noise), even with compensation. A pink background indicates low quality (not recommended).

##### Examples:

Vertical pixels (2484 for High quality)  For this system, which uses an LVT color film chart with Vertical Field of View = 140mm (5.51 inches), the maximum number of vertical pixels where MTF @ fNyq ≥ 0.9 (so that no MTF compensation is needed) is 2584 (equivalent to 10 Megapixels for a 3:2 aspect ratio).

V-pxls/cm (184.6 for High quality)  If you have a camera with 4000 vertical pixels, the minimum chart size for MTF @ fNyq ≥ 0.9 would be 4000/184.6 = 21.67cm = 8.53 inches. Since this is a little larger than the maximum dimension for color film LVT charts, which have a 9.25×7.75 inch printable area, MTF compensation would be required for accurate results.

• Chart Quality Index (CQInn), used prior to Imatest 5.1, is the number of vertical pixels where MTF @ Nyquist = nn% (typical values are 90, 70, and 50%). It is the same number as the Vertical pixels column in the above table.

$$CQI_{nn} = 2 \times \text{test chart MTFnn (cycles/object mm)} \times \text{height in mm}$$

where height is the typical vertical field of view for SFRplus (1.1 * the bar-to-bar distance) or the vertical crop height of the chart active area for most other test charts. Cycles/object mm is defined on the chart. CQI90 was the standard value for high quality images. We no longer use CQI because the description on the web page is difficult to follow and the name is not very descriptive.

• The old (pre-2018) Megapixel suitability number, which was defined as

$$\text{Megapixel suitability} = 2 \times (0.5(\text{MTF50}) + 0.35(\text{MTF70}) + 0.15(\text{MTF50}))\times \text{vertical chart height (mm)}$$

where MTFnn has units of Cycles/Object mm. This number appears above the Settings boxes in the Chart Quality Calculator. In the above image, it is

Old Mpxl suitability: V pxls= 3567;  19.1Mpxls (3:2)     (abbreviated because of limited space).

The old Megapixel suitability is 3567 vertical pixels = 19.1 Megapixels for a 3:2 aspect ratio. This is very close to the values for Quality level (old Mpxl limit) (MTF @ Nyquist frequency = 0.77) = 3645 vertical pixels = 17.7 Mpxls (at 3:2 aspect ratio). This is a fairly conservative estimate of the chart limit, where MTF compensation will only make a small improvement.

#### Results for a specific imaging system

When the Chart Quality Calculator is opened, chart MTF is displayed in frequency units of cycles per object mm on the chart (shown above). This is for the chart itself (independent of the imaging system), except for the vertical Nyquist frequency line, which is calculated relative to the sensor.

The Chart Quality Calculator can also display results for an imaging system characterized by  pixel size (μm per pixel), magnification, and sensor height in mm.

By clicking on the frequency toggle button at the bottom-left of the plot (which originally displays  Frequency (Cycles/Obj mm on the chart) , the display can be changed to Cycles/Pixel on the sensor, shown on the right. This plot directly indicates the effect of the chart on MTF at spatial frequencies on the sensor. As we indicated above, MTF at the Nyquist frequency (fNyq = 0.5 C/P) and also the half Nyquist frequency (0.25 C/P, which is in the neighborhood of MTF50 for typical sharp imaging systems) are good indicators for the chart quality for this system.

Results for a specific system with frequency in C/P on the image sensor

Results for the system, which is defined by the pixel size (μm per pixel), magnification, and sensor height in mm (entered on the lower-right), are displayed in maroon to the right of the MTF plot. MTF = 0.746 @ Nyquist = 0.965 @ Nyq/2 indicate that the chart is good enough to be used without MTF compensation in this system, though MTF compensation is recommended for more accurate results.

#### Limitations

Measurements are not reliable where the projected chart MTF is lower than 0.3. The frequency where this happens (MTF30) should always be above the Nyquist frequency fNyq. If possible it should be above 2* fNyq.

Measurement accuracy near the boundaries of strongly barrel-distorted (fisheye) lenses is affected by reduced magnification in the radial direction, which affects the sharpness of tangential edges. We may fix this in the future. This is not an issue with moderately distorted rectilinear (normal) lenses.

#### Appendix. Chart MTF measurement

Most users won’t be measuring chart quality themselves. They’ll use the measurement results in Chart MTF compensation files provided by Imatest (downloadable from www.imatest.com/docs/mtf-compensation/#compfiles ). Those users can skip this section.

Chart MTF is measured from images of slanted-edges, printed at between 4:1 and 10:1 contrast on various media (inkjet paper, photographic paper, B&W or color film, or Chrome on Glass). These media are both transmissive and reflective and have a wide range of sharpness.

1. Photograph the chart at the appropriate magnification, making sure the magnification is accurately measured and recorded (it can be included in the file name). The magnification should be high enough so the measured MTF is limited by the chart, not by the camera. Measured chart MTF50 should be under 0.1 cycles/pixel to minimize the effects of image processing on the results. This generally requires a high quality prime macro lens. We have used a Canon EOS-6D DSLR camera with Canon MP-E 65mm f/2.8 1-5x marco and EF 100mm f/2.8 macro USM lenses. With this gear we recommend 0.5x or 1x for inkjet charts, which are quite rough, and 4x or more for photographic (film and paper) and Chrome on Glass (CoG) charts. This setup may not do justice to the exceptional resolution of CoG charts.
2. Run the image in SFR with the following settings: MTF plot units = Cycles/Object mm. Enter Pixel size (6.5 um/pixel for the EOS-6D) and Magnification. Check ROI detection & plot extra smoothing. Make sure Gamma is set correctly (it’s 1 for raw files; ~0.5 for standard color space files). Max MTF plot Freq should be set ≤ 0.5x Nyquist (may vary). Chart MTF compensation settings (to be used later) should be unchecked. In the ROI Options window (accessible from the Imatest main window) SFR ROI filtering should be set to None. The region should be large enough so that random noise is not too high. (Since noise can be a problem with inkjet charts, ROI size may be 600×1000 pixels or larger.)
3. If the settings are correct, Imatest will calculate a fit to the equation,
$$MTF_{chart}(f) = e^{-a_1 f – (a_2 f)^2}$$ where f has units of cycles/object mm (C/Obj mm). This equation fits a variety of curve shapes, and can handle response bumps, as shown above. It is shown as a dotted cyan line …… on the right— difficult to see because it’s coincident with thick black MTF curve for the Y (luminance) channel for MTF > 0.3. It is matched to the data only for f ≤ MTF30, i.e., only where MTF is greater than 0.3 (30%).
4. The spatial frequency projected on the image sensor equals the spatial frequency on the chart (object) divided by the magnification. The projected chart MTF on the image sensor is expressed in native units of cycles/pixel (C/P), using
$$f(\text{C/Obj mm}) = f(C/P) \times \text{magnification} \times \text{pixels/mm}$$

Pixels/mm is usually derived from the pixel pitch (μm per pixel), which is entered in the settings window.
pixels/mm = 1000 / (pixel pitch (um/pixel))
$$MTF_{chart-projected}(f) = MTF_{chart}(f(C/P) \times \text{magnification} \times \text{pixels/mm})$$
The equation for the compensated MTF is
$$\displaystyle MTF_{chart-compensated} = \frac{MTF_{measured}}{\text{max}(MTF_{chart-projected},\text{ } 0.3)}$$

5. MTFchart-compensated is also called MTFdiv because it is used to divide MTFmeasured. The minimum value of the denominator must be greater than 0.3 because smaller values can cause an excessive noise boost. The frequency where projected chart MTF drops to 0.3 should be outside the range of interest for the measurement— well above the Nyquist frequency  fNyq if possible and ideally above 2* fNyq. The results will be displayed in the command window and copied to the clipboard (for the last ROI-only). Here is a sample for this image.
— MTF coefficients x for deconvolution (will be copied to clipboard)—
-0.00968, 0.04781
from C:\imatest\Data\Misc\Chart_scans\Color LVT Film 4x 4-1\Vertical\ColorLVT_65mm_f4_s1-13_5992.tiff
MTF50 = 0.03259 C/P = 20.06 Cycles/Object mm. Magnification = 4
( MTF = exp(-x(1)*f-(x(2)*f).^2) for f in cycles/object mm. )
MTF90,70,50,30 = 9.23 14.79 19.66 25.17 Cy/Obj mm

The lines shown in blue should be copied and pasted into a file, which will be saved with the CSV extension. Only the first line (-0.00968, 0.04781) contains data (coefficients a1 and a2 from the MTFchart(f) equation, above. The rest is comments that can be useful for verifying that you have the correct settings.