Sharpness

Image sharpness

Sharpness is arguably the most important photographic image quality factor because it's the factor that determines the amount of detail an imaging system can reproduce. But 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 (assuming a 0.5 millimeter long image of the pattern formed by a typical DSLR lens). It is blurred. All lenses, even the finest, blur images to some degree. Poor lenses blur images more than fine ones.

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: 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

• the original sine pattern
• the sine pattern with lens blur
• the original bar pattern
• the bar pattern with lens blur

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.

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 (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.

One advantage of the slanted edge test is that the camera-to-target distance isn't 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° can have numerical problems.

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

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.

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.

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. The Nyquist frequency is displayed as a vertical blue line.

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.

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.

Lens-type MTF plot (similar to MTF plots from the Canon, Nikon, and Zeiss websites.

Interpreting MTF50

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

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 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.

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

• Frequency and spatial domain plots convey similar information, but in a different form. A narrow edge in spatial domain corresponds to a broad spectrum in frequency domain (extended frequency response), and vice-versa.
• Sensor response above the Nyquist frequency is garbage— aliasing, visible as Moire patterns of low spatial frequency. In Bayer sensors (all sensors except Foveon) Moire patterns appear as color fringes. Moire in Foveon sensors is far less bothersome because it's monochrome and because the effective Nyquist frequency of the Red and Blue channels is lower than for Bayer sensors.
• Since MTF is the product of the lens and sensor response, demosaicing algorithm, and sharpening, and since sharpening typically boosts MTF at the Nyquist frequency, the MTF at and above the Nyquist frequency is not an unambiguous indicator of aliasing problems. It may, however, be interpreted as a warning that there could be problems.
• Results are calculated for the R, G, B, and Luminance (Y) channels, where Y = 0.3*R + 0.59*G + 0.11*B. The Y channel is normally displayed in the foreground, but any of the other channels can selected. All are included in the .CVS output file.
• Horizontal and vertical resolution can be different for CCD sensors, and must be measured separately. They're nearly identical for CMOS sensors. Recall, horizontal resolution is measured with a vertical edge and vertical resolution is measured with a horizontal edge.
• Resolution is not the only important criterion for evaluating image quality. Noise is also important. The Shannon information capacity is an experimental metric that combines the two.

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

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.