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Image sharpness

Sharpness is arguably the most important photographic image quality factor because it determines the amount of detail an imaging system can reproduce. It's not the only important factor; Imatest measures a great many others.

Sharpness is defined by the boundaries between zones of different tones or colors. It is illustrated by the bar pattern of increasing spatial frequency, below. The top portion represents a pattern that could be used to test a camera/lens combination. It is sharp; its boundaries are crisp, not gradual. The bottom portion illustrates how the pattern is degraded after it passes through a lens. It is blurred. All lenses, even the finest, blur images to some degree. Poor lenses blur images more than fine ones.

Bar pattern of increasing spatial frequency, showing blur
                     Bar pattern: Original (top); with lens degradation (bottom)

One way to measure sharpness is to use the rise distance of the edge, for example, the distance (in pixels, millimeters, or fraction of image height) for the pixel level to go from 10% to 90% of its final value. This is called the 10-90% rise distance. Although rise distance is a good indicator of image sharpness, it has an important limitation. There is no simple way to calculate the rise distance of a complete imaging system from the rise distance of its components, for example, from a lens, digital sensor, and software sharpening algorithm.

To get around this problem, measurements are made in frequency domain, where frequency is measured in cycles or line pairs per distance (millimeters, inches, pixels, or image height). Line pairs per millimeter (lp/mm) is the most common spatial frequency unit for film, but cycles/pixel (C/P)  and line widths/picture height (LW/PH) are more convenient for digital sensors.

The image below is a sine wave— a pattern of pure tones— that varies from low to high spatial frequencies. The top portion is the original sine pattern. The bottom portion illustrates lens degradation, which reduces pattern contrast at high spatial frequencies.

Sine pattern of increasing spatial frequency, showing blur
Sine pattern: Original (top); with lens degradation (bottom)

The relative contrast at a given spatial frequency (output contrast/input contrast) is called the Modulation Transfer Function (MTF) or Spatial Frequency Response (SFR). It is the key to measuring sharpness.

Modulation Transfer Function (MTF)

Modulation Transfer Function (MTF), which is generally identical to Spatial Frequency Response (SFR), can be explained using the illustration below.


Sine and bar patterns, amplitude plot, and MTF plot

The upper plot displays

Lens blur causes contrast to drop at high spatial frequencies.

The middle plot displays the luminance (":modulation"; V in the equation below) of the bar pattern with lens blur (the red curve). Contrast decreases at high spatial frequencies. The modulation of the sine pattern (which consists of pure frequencies) is used to calculate MTF.

The lower plot displays the corresponding MTF (SFR) curve (the blue curve), which is defined below.

By definition, the low frequency MTF limit is always 1 (100%). For this lens, MTF is 50% at 61 lp/mm and 10% at 183 lp/mm.

Both frequency and MTF are displayed on logarithmic scales with exponential notation (100 = 1; 101 = 10; 102 = 100, etc.). Amplitude is displayed on a linear scale.


The beauty of using MTF (Spatial Frequency Response) is that the MTF of a complete imaging system is the product of the the MTF of its individual components.

The equation for MTF is derived from the sine pattern contrast at spatial frequency f, C(f ), where

     C(f ) = (Vmax- Vmin) / (Vmax+ Vmin)     for luminance ("modulation") V.

     MTF(f) = 100% C(f) / C(0)             This normalizes MTF to 100% at low spatial frequencies

Green is for geeks. Do you get excited by a good equation? Were you passionate about your college math classes? Then you're probably a math geek— a member of a misunderstood but highly elite fellowship. The text in green is for you. If you're normal or mathematically challenged, you may skip these sections. You'll never know what you missed.
MTF is related to edge response by a mathematical operation known as the Fourier transform. MTF is the Fourier transform of the impulse response— the response to a narrow line, which is the derivative (d/dx) of the edge response. Fortunately, you don't need to understand Fourier transforms or calculus to understand MTF.

USAF 1951 chart
USAF 1951 chart

Traditional "resolution" measurements involve observing an image of a bar pattern (usually the USAF 1951 chart), and looking for the highest spatial frequency (in lp/mm) where the bars are visibly distinct. This measurement, called "vanishing resolution", corresponds to an MTF of about 5-10%. Because this is the spatial frequency where image information disappears— where it isn't visible, it is not a good indicator of image sharpness. (It's Where the Woozle Wasn't in the world of Winnie the Pooh.) It's also poorly suited for computer analysis.

Experience has shown that the best indicators of image sharpness are the spatial frequencies where MTF is 50% of its low frequency value (MTF50) or 50% of its peak value (MTF50P).

MTF50 or MTF50P are good parameters for comparing the sharpness of different cameras and lenses for two reasons: (1) Image contrast is half its low frequency or peak values, hence detail is still quite visible. The eye is relatively insensitive to detail at spatial frequencies where MTF is low: 10% or less. (2) The response of most cameras falls off rapidly in the vicinity of MTF50 and MTF50P. MTF50P may better for strongly sharpened cameras that have "halos" near edges and corresponding peaks in their MTF response.

Although MTF can be estimated directly from images of sine patterns (using Rescharts Log Frequency, Log F-Contrast, and Star Chart), a sophisticated technique, based on the ISO 12233 standard, "Photography - Electronic still picture cameras - Resolution measurements," provides more accurate and repeatable results. A slanted-edge image, described below, is photographed, then analyzed by Imatest SFR or SFRplus.

Origins of Imatest SFR  The algorithms for calculating MTF/SFR were adapted from a Matlab program, sfrmat, written by Peter Burns () to implement the ISO 12233 standard. Imatest SFR incorporates numerous improvements, including improved edge detection, better handling of lens distortion, a nicer interface, and far more detailed output. The original Matlab code was available on the I3A ISO tools download page by clicking on ISO 12233 Slant Edge Analysis Tool sfrmat 2.0. In comparing sfrmat 2.0 results with Imatest, note that if no OECF (tonal response curve) file is entered into sfrmat, it assumes that there is no tonal response curve, i.e., gamma = 1. In Imatest, gamma is set to a default value of 0.5, which is typical of digital cameras. To obtain good agreement with sfrmat, you must set gamma to 1.

The slanted-edge measurement for Spatial Frequency Response

Two Imatest modules measure MTF using the slanted-edge technique: SFR and SFRplus.

ISO 12233 chart, showing horizontal and vertical edges
ISO 12233 chart (left) and typical SFR region selection (right)

Imatest SFR measures MTF from slanted-edges in a wide variety of charts, including composite targets similar to those described in The Imatest Test Lab, SFRplus charts, the ISO 12233 test chart, shown on the right, or derivatives like the Applied Image QA-77 or the less expensive Danes-Picta DCR3 chart.

Two regions in the ISO 12233 chart are indicated by the red and blue arrows. ISO 12233 charts are used in imaging-resource.com and dpreview.com camera reviews. A typical region is shown on the right: a crop of a vertical edge (slanted about 5 degrees) used to calculate horizontal MTF response.

Slanted-edge test charts may be purchased from Imatest or created with Imatest Test Charts.

Briefly, the slanted edge method calculates MTF by finding the average edge (4X oversampled using a clever binning algorithm), differentiating it (this is the Line Spread Function (LSF)), then taking the absolute value of the fourier transform of the LSF. The edge is slanted so the average is derived from a distribution of sampling phases (relationships between the edge and pixel locations). The algorithm is described in detail here.

The slanted-edge method has several advantages. The camera-to-target distance is not critical; it doesn't enter into the equation that converts the image into MTF response. Slanted-edges also take up much less space than sine patterns and are less sensitive to noise. Imatest Master can calculate MTF for edges of virtually any angle, though exact vertical, horizontal, and 45° should be avoided because of sampling phase sensitivity.

SFRplus chart
SFRplus chart with 5x9 grid of squares

Imatest SFRplus measures MTF (and many other image quality parameters) from the specially-designed SFRplus chart, which can be purchased from Imatest (recommended) or created using Imatest Test Charts (not recommended; a widebody printer, good printing skills, and knowledge of color management are required).

SFRplus offers numerous advantages over the ISO 12233 measurements: lower contrast improves the accuracy of the results, more edges (less wasted space) make it possible to map MTF over the image surface, and region detection is highly automated.

How to test lenses with Imatest has a good summary of how to measure MTF using SFRplus.

Noise reduction (modified apodization technique)

A powerful noise reduction technique called modified apodization is available for slanted-edge measurements (SFR and SFRplus) starting with Imatest 3.7. This technique makes virtually no difference in low-noise images, but it can significantly improve measurement accuracy for noisy images, especially at high spatial frequencies (f > Nyquist/2). It is applied when the MTF noise reduction (modified apodization) checkbox is checked in the SFR input dialog box or the SFRplus More settings window.

Note that we recommend keeping it enabled even though it is NOT a part of the ISO 12233 standard. If the ISO standard checkbox is checked (at the bottom-left of the dialog boxes), noise reduction is not applied.

The strange word apodization* comes from "Comparison of Fourier transform methods for calculating MTF" by Joseph D. LaVeigne, Stephen D. Burks, and Brian Nehring, available on the Santa Barbara Infrared website. The fundamental assumption is that all important detail (at least for high spatial frequencies) is close to the edge. Tthe original technique involves setting the Line Spread Function (LSF) to zero beyond a specified distance from the edge. The modified technique strongly smooths (lowpass filters) the LSF instead. This has much less effect on low frequency response than the the original technique, and allows tighter boundaries to be set for better noise reduction.

*Pedicure would be a better name for the new technique, but it might confuse the unititiated.

Modified apodization noise reduction- explanation
Modified apodization: original noisy averaged Line Spread Function (bottom; green),
smoothed (middle; blue), LSF used for MTF (top; red)

Algorithm

The benefits of modified apodization noise reduction are shown below for an image with strong (simulated) white noise.

Modified Apodization noise reduction: before and after
Modified apodization noise reduction on a noisy image: without (L) and with (R)

MTF Measurement Matrix

Imatest has many ways of measuring MTF, each of which tends to give different results in consumer cameras because image processing, which strongly affects MTF measurements, depends on local scene content, which is rarely constant throughout an image. Sharpening (high frequency boost) tends to be maximum near contrasty lines or edges while noise reduction (high frequency cut, which usually obscures fine texture) tends to be maximum in their absence. For this reason MTF measurements can be very different with different test charts.

Measurement Advantages / Disadvantages / Sensitivity
Primary use & comments
Slanted-edge
(SFR/SFRplus)
Efficient use of space makes it possible to create a detailed map of MTF response. Fast, automated region detection in SFRplus. Fast calculations. Relatively immune to noise (highly immune if noise reduction is applied).
May give optimistic results in systems with strong sharpening and noise reduction (i.e., it can be fooled, especially with high contrast (≥ 10:1) edges.
Strongly sensitive to sharpening for high contrast (≥10:1) edges; less sensitive for low contrast edges (≤2:1). Insensitive to Noise reduction

This is the primary MTF measurement in Imatest.

Most efficient pattern for lens and camera testing, especially where a MTF response map is required.

Log frequency Calculated from first principles. Displays color moire.
Sensitive to noise.
Primarily used as a check on other methods, which are not calculated from first principles.
Log f-Contrast Sensitive to noise.
Sensitivity to sharpening decreases and sensitivity to noise reduction increases from top (most contrasty) to bottom (least contrasty).
Illustrates how signal processing varies with image content (feature contrast).
Siemens star Slow, requires significant real estate.
Low to moderate sensitivity to sharpening and noise reduction.
Recommended for general testing by Image Engineering, but spatial detail is limited to a 3x3 or 4x3 grid.
Random (scale-invariant) Reveals how well fine detail (texture) is rendered: system response to software noise reduction.
Insensitive to sharpening, Strongly sensitive to Noise reduction
Measures a camera's ability to render fine detail (texture), i.e., low contrast, high spatial frequency image content.
Wedge Makes use of wedge patterns on the ISO 12233 chart. MTF is not accurate at Nyquist and half-Nyquist frequencies. Should never be used as a primary MTF measurement.
Measures "vanishing resolution" from CIPA DC-003: where lines start disappearing in wedge patterns, most commonly in the ISO 12233 chart.
MTF Measurement Matrix

Spatial frequency units

Most readers will be familiar with temporal frequency. The frequency of a sound— measured in Cycles/Second or Hertz— is closely related to its perceived pitch. The frequencies of radio transmissions (measured in kilohertz, megahertz, and gigahertz) are also familiar. Spatial frequency is similar: it is measured in cyles (or line pairs) per distance instead of time. Spatial frequency response is closely analogous to temporal (e.g., audio) frequency response. The more extended the response, the more detail can be conveyed.

Units of spatial frequency should be selected based on the application, for example, is the measurement intended to determine how much detail a camera can reproduce or how well the pixels are utilized?

Film camera lens tests used line pairs per millimeter (lp/mm). This worked fine for comparing lenses because all 35mm cameras have the same 24x36 mm picture size. But digital sensor sizes varies widely, from under 5 mm diagonal in cameraphones to 43 mm diagonal for full-frame DSLRs— even larger for medium format backs. For this reason, Line widths per picture height (LW/PH) is recommended for measuring the total detail a camera can reproduce. LW/PH is equal to 2 * lp/mm * (picture height in mm).

Another useful measure of spatial frequency is cycles per pixel (C/P). This gives an indication of how well individual pixels are utilized. There is no need to use actual distances (millimeters or inches) with digital cameras, although such measurements are available in Imatest SFR.

Summary of Spatial frequency units
Unit Application
Cycles/Pixel (C/P) Shows how well pixels are utilized
Cycles/Distance
(cycles/mm or cycles/inch)
Used for comparing resolution in the old days of standard film formats (e.g., 24x36mm for 35mm film).  Pixel spacing must be entered.
Line Widths/Picture Height (LW/PH) Measures overall image sharpness. Line Widths is traditional for TV.
Note that 1 Cycle = 1 Line Pair (LP) = 2 Line Widths (LW).
Line Pairs/Picture Height (LP/PH) Measures overall image sharpness. Used by dpreview.com.
Cycles/milliradian Angular frequency. 0.001 * (cycles/mm) * (lens focal length in mm).  Pixel spacing and focal length must be entered. Focal length is usually included in EXIF data, but may be entered manually.
Cycles/degree Angular frequency. π/180 * (cycles/mm) * (lens focal length in mm).  Pixel spacing and focal length must be entered. Useful for comparing camera systems to the human eye, which has an MTF50 of roughly 20 cycles/degree (depending on the individual's eyesight and illumination).

Different units scale differently with image sensor and pixel size.

The use of Picture Height gives a slight advantage to compact digital cameras, which have an aspect ratio (width:height) of 4:3, compared to 3:2 for digital SLRs. Compact digital cameras have slightly more vertical pixels for a given number of total pixels. For example, a 5.33 megapixel compact digital camera would have 2000 vertical pixels— as many as a 6 megapixel DSLR.

Imatest SFR and SFRplus results

The average edge and MTF plot from Imatest SFR is shown below. SFRplus produces very similar results.


SFR results from an SFRplus image for the Canon EOS-40D.

(Top-left)  A narrow image that illustrates the tones of the averaged edge. It is aligned with the edge profile (spatial domain) plot, immediately below.

(Middle-left)  Spatial domain plot:  The average edge profile (linearized, i.e., proportional to light energy). A key result is the 10-90% edge rise distance, shown in pixels and in the number of rise distances per Picture Height. Other parameters include overshoot and undershoot (if applicable). This plot can optionally display the line spread function (LSF: the derivative of the edge), or the edge in pixels (gamma-encoded).

(Bottom-left)  Frequency domain plot:  The Spatial Frequency Response (MTF), shown to twice the Nyquist frequency. The key result is MTF50, the 50% MTF frequency, which corresponds to perceived image sharpness. It is given in units of cycles per pixel (C/P) and Line Widths per Picture Height (LW/PH). Other results include MTF at Nyquist (0.5 cycles/pixel; sampling rate/2), which indicates the probable severity of aliasing and user-selected secondary readouts. The Nyquist frequency is displayed as a vertical blue line. The diffraction-limited MTF response is shown as a pale brown dashed line when the pixel spacing is entered (manually) and the lens focal length is entered (usually from EXIF data, but can be manually entered).

For this camera, which is moderately sharpened, MTF50P (displayed only when Standardized sharpening display is unchecked) is identical to MTF50.

SFR Results: MTF (sharpness) plot describes this Figure in detail.

MTF curves and Image appearance contains several examples illustrating the correlation between MTF curves and perceived sharpness.

Here are two displays that illustrate some of the many capabilities of SFRplus. Other displays include MTF, Chromatic Aberration and noise statistics for individudual regions, and image and geometry (including distortion), color error, tonal response and uniformity profiles for the image as a whole.

SFRplus 3D plot
3D Plot for MTF50 (one of many available results).
3D plots have a great many display options;
they can be rotated freely or viewed from the top.
SFRplus lens-type MTF plot
Lens-type MTF plot
(similar to MTF plots from the
Canon, Nikon, and Zeiss websites.

Diffraction and Optimum Aperture

Lens sharpness is limited by two basic factors.

  1. Lens Aberrations  Imperfections in optical systems that arise from a number of causes— different bending of light at different wavelengths, the inability of spherical surfaces to provide clear images over large fields of view, changes in focus for light rays that don't pass through the center of the lens, and many more. Aberration correction is the primary purpose of sophisticated lens design and manufacturing; It's what distinguishes excellent from mediocre optical design.

    Lens aberrations tend to be worst at large apertures (small f-stop numbers). Aberrations vary greatly for different lenses (and even among of different samples of the same lens); quality control is often quite sloppy.
  2. Diffraction,  A fundamental physical property that blurs images. Diffraction is caused by the bending of light waves near boundaries.

    The smaller the aperture (the larger the f-stop number), the worse the diffraction blur. Since it's a fundamental physical effect, it's the same for all lenses. Lens performance doesn't vary a lot at small apertures (large f-stop numbers).

If you're not familiar with this terminology, a lens's f-stop number is equal to its focal length divided by its aperture diameter. In the classic f-stop sequence {1  1.4  2  2.8  4  5.6  8  11  16  22  32  45  64  90  128  etc.}, each stop admits half the light of the previous stop while the f-stop number is multiplied by the square root of 2 (1.414). When a photographer says, "I increased the exposure by one f-stop", he means he went down the sequence by one step, e.g., changed the aperture from f/8 to f/5.6.

Batchview sample result
Batchview result

As a result of these two phenomena, lenses tend to have an optimum aperture where they are sharpest, typically around 2-3 f-stops below a lens's maximum aperture. The optimum is fairly broad: your aperture can usually be off by up to two f-stops away without serious sharpness loss.

You can find the optimum aperture by running a batch of images (Imatest SFRplus recommended) taken at different apertures, then entering the combined output (a CSV file) into Batchview. A set of images taken at f/4.5-f/22 is shown on the right: The bars show MTF50 in Line Widths per Picture Height (LW/PH) for the weighted mean (black), center area (red), part-way area (green) and corners (blue). The procedure is described in detail here. For this lens the optimum aperture is 3-4 stops from the maximum. Edge sharpness is unimpressive. It's not one of Canon's better efforts.

diffraction plot
MTF plots showing diffraction-limited MTF
(as a pale brown dotted line)

Diffraction-limited MTF is displayed as a pale brown dotted curve in the MTF figures produced by SFR and SFRplus when the pixel spacing (usually given in microns) has been manually entered in the appropriate input dialog box. The curve on the left is for the Canon EOS-40D (5.7 micron pixel spacing) with the lens set at f/22— a small aperture that should only be used with large depth of field is required and sharpness can be sacrificed.

The equation for diffraction-limited MTF can be found in Diffraction Modulation Transfer Function from the SPIE OPTIPEDIA, David Jacobson's Lens Tutorial, and normankoren.com.

The diffraction cutoff frequency is   fcutoff = 1/(λ N)

where λ is the wavelength and N is the f-stop number. λ is typically 0.555 microns (0.000555 mm) for visible light, but it can be changed for cameras with different spectral response (like Infrared).

Let s = f/fcutoff .  The diffraction-limited MTF is

MTFdiffraction-ltd(s) = 2/π (arccos(s) -sqrt(1-s2 ))      for s < 1

             = 0     for s >= 1

The figure is shown with a Data Cursor Datatip, which allows you to examine plot or image pixel values. It is available in all figures and interactive GUIs in Imatest 3.6+.

Lens MTF response can never exceed the diffraction limited response, but system MTF response almost always exceeds it at medium spatial frequencies as a result of sharpening, which is (and should be) present in most digital imaging systems.

In addition to lens response, system MTF response is affected by the sensor (which has a null at 1 cycle/pixel), the anti-aliasing filter (designed to suppress energy above 0.5 cycles/pixel), and signal processing (which can be very complex— it can be different in different regions of an image).

Interpreting MTF50

This section was written before the addition of SQF (Subjective Quality Factor)
to Imatest (November 2006). SQF allows a more refined estimate of perceived print sharpness.

What MTF50 do you need?  It depends on print size. If you plan to print gigantic posters (20x30 inches or over), the more the merrier. Any high quality 4+ megapixel digital camera (one that produces good test results; MTF50(corr) > 0.3 cycles/pixel) is capable of producing excellent 8.5x11 inch (letter-size; A4) prints. At that size a fine DSLR wouldn't offer a large advantage in MTF. With fine lenses and careful technique (a different RAW converter from Canon's and a little extra sharpening), my 6.3 megapixel Canon EOS-10D (corrected MTF50 = 1340 LW/PH) makes very good 12x18 inch prints (excellent if you don't view them too closely). Prints are sharp from normal viewing distances, but pixels are visible under a magnifier or loupe; the prints are not as sharp as the Epson 2200 printer is capable of producing. Softness or pixellation would be visible on 16x24 inch enlargements. The EOS-20D has a slight edge at 12x18 inches; it's about as sharp as I could ask for. There's little reason go go to a 12+ megapixel camera lie the EOS 5D, unless you plan to print larger. Sharpness comparisons contains tables, derived from images downloaded from two well-known websites, that compare a number of digital cameras. Several outperform the 10D.

The table below is an approximate guide to quality requirements. The equation for the left column is

MTF50(Line Widths ⁄ inch on the print) =
    MTF50(LW ⁄ PH)     
Print height in inches

MTF50 in
Line Widthsinch
on the print
Quality level— after post-processing, which may include some additional sharpening
150 Excellent— Extremely sharp at any viewing distance. About as sharp as most inkjet printers can print.
110 Very good— Large prints (A3 or 13x19 inch) look excellent, though they won't look perfect under a magnifier. Small prints still look very good.
80 Good— Large prints look OK when viewed from normal distances, but somewhat soft when examined closely. Small prints look soft adequate, perhaps, for the "average" consumer, but definitely not "crisp."

Example of using the table: My Canon EOS-10D has MTF50 = 1335 LW/PH (corrected; with standardized sharpening). When I make a 12.3 inch high print on 13x19 inch paper, MTF50 is 1335/12.3 = 108 LW/in: "very good" quality; fine for a print that size. Prints look excellent at normal viewing distances for a print this size.

This approach is more accurate than tables based on pixel count (PPI) alone (though less refined than SQF, below). Pixel count is scaled differently; the numbers are around double the MTF50 numbers. The EOS-10D has 2048/12.3 = 167 pixels per inch (PPI) at this magnification. This table should not be taken as gospel: it was first published in October 2004, bandit may be adjusted in the future.

Subjective Quality Factor (SQF)

SQF for EOS-10D
SQF as a function of picture height

MTF is a measure of device or system sharpness, only indirectly related to the sharpness perceived when viewing a print. A more refined estimate of perceived print sharpness must include assumptions about viewing distance (typically proportional to the square root of print height) and the human visual system (the human eye's Contrast Sensitivity Function (CSF)). Such an formula, called Subjective Quality Factor (SQF) was developed by Eastman Kodak scientists in 1972. It has been verified and used inside Kodak and Polaroid, but it has remained obscure until now because it was difficult to calculate. Its only significant public exposure has been in Popular Photography lens tests. SQF was added to Imatest in October 2006.

A portion of the Imatest SFR SQF figure for the EOS-10D is shown on the right. SQF is plotted as a function of print size. Viewing distance (pale blue dashes, with scale on the right) is assumed to be proportional to the square root of picture height. SQF is shown with and without standardized sharpening. (They are very close, which is somewhat unusual.) SQF is extremely sensitive to sharpening, as you would expect since sharpening is applied to improve perceptual sharpness.

The table below compares SQF for the EOS-10D with the MTF50 from the table above.

MTF50 in
Line Widthsinch
on the print
Corresponding print height for the EOS-10D (MTF50 = 1335 LW/PH) SQF at this print height Quality level— after post-processing, which may include some additional sharpening. Overall impression from viewing images at normal distances as well as close up.
150 8.9 inches = 22.6 cm 93 Excellent— Extremely sharp.
110 12.1 inches = 30.8 cm 90 Very good.
80 16.7 inches = 42.4 cm 86 Good— Very good at normal viewing distance for a print of this size, but visibly soft on close examination.

An interpretation of SQF is give here. Generally, 90-100 is considered excellent, 80-90 is very good, 70-80 is good, and 60-70 is fair. These numbers (which may be changed as more data becomes available) are the result of "normal" observers viewing prints at normal distances (e.g.., 30-34 cm (12-13 inches) for 10 cm (4 inch) high prints). The judgments in the table above are a bit more stringent— the result of critical examination by a serious photographer. They correspond more closely to the "normal" interpretation of SQF when the viewing distance is proportional to the cube root of print height (SQF = 90, 86, and 80, respectively), i.e., prints are examined more closely than the standard square root assumption.

An SQF peak over about 105 may indicate oversharpening (strong halos near edges), which can degrade image quality. SQF measurements are more valid when oversharpening is removed, which is accomplished with standardized sharpening.

Some observations on sharpness

The ideal response would have high MTF below the Nyquist frequency and low MTF at and above it.

Slanted edge algorithm (calculation details)
The MTF calculation is derived from ISO standard 12233. Some details are contained in Peter Burns' SFRMAT 2.0 User's Guide, which can be downloaded from the I3A ISO tools download page by clicking on Slant Edge Analysis Tool sfrmat 2.0. The Imatest calculation contains a number of refinements and enhancements, including more accurate edge detection and compensation for lens distortion (which could affect MTF measurements). The original ISO calculation is performed when the ISO standard SFR checkbox in the SFR input dialog box is checked. It is normally left unchecked. Additional details of the calculation can be found in Appendix C, Video Acquisition Measurement Methods (especially pp. 102-103), of the Public Safety SoR (Statement of Requirements) volume II v 1.0 (6 MB download), released by SAFECOM, prepared by ITS (a division of NTIA, U.S. Department of Commerce).

Links

How to Read MTF Curves  by H. H. Nasse of Carl Zeiss. Excellent, thorough introduction. 33 pages long; requires patience. Has a lot of detail on the MTF curves similar to the Lens-style MTF curve in SFRplus. Even more detail in Part II. Their (optical) MTF Tester K8 is of some interest.

Understanding MTF from Luminous Landscape.com has a much shorter introduction.

Understanding image sharpness and MTF  A multi-part series by the author of Imatest, mostly written prior to Imatest's founding. Moderately technical.

Bob Atkins has an excellent introduction to MTF and SQF. SQF (subjective quality factor) is a measure of perceived print sharpness that incorporates the contrast sensitivity function (CSF) of the human eye. It will be added to Imatest Master in late October 2006.

Spatial Frequency Response of Color Image Sensors: Bayer Color Filters and Foveon X3 by Paul M. Hubel, John Liu and Rudolph J. Guttosch, Foveon, Inc., Santa Clara, California.  Uses slanted edge testing.

Optikos makes instruments for measuring lens MTF. Their 64 page PDF document, How to Measure MTF and other Properties of Lenses, is of particular interest.

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