Understanding image sharpness part 3:
Printers and prints
by Norman Koren

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In this page we discuss printers and prints and how to characterize their sharpness and resolution. We deal with the issue of how many pixels per inch are required for a sharp print.

Note (November 2004): This page is out of date; it hasn't been updated for my Epson 2200 printer and my (superior) Epson 3200 scanner. I have, however, measured the sharpness of the Epson 2200 using the Imatest program, which employs a superior technique— simpler to run and much more accurate. I've also discussed print sharpness in Sharpness: what is it and how is it measured?, particularly in the section on Interpretation of MTF50.

I owe an acknowledgment to Peter Nelson , whose excellent study of printer resolution , discussed in a photo.net post , gave me the idea of pursuing this line of thought. When I wrote this (May 2001) I knew of no standard for printer sharpness and/or resolution. I still don't.

Printer / print sharpness

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• How can we define the sharpness of prints and printers?
• How many image pixels per inch are needed to make a sharp print?
• How much of an advantage does a 4000 dpi scanner have over a less expensive 2400-2800 dpi scanner for various print magnifications?

• The printer's dpi specification is meaningless ; it is merely the stepper motor pitch. Epson specifies the "resolution" of its new 1280 printer as 2880 x720 dpi. Horsefeathers!  (For non-English speakers, "Horsefeathers" is the title of an old Groucho Marx film, implying the ridiculous or absurd.) It takes several dots to reproduce one full toned pixel. Reviews of the Epson 1280 noted that actual resolution (i.e., the visual appearance) at the 2880 dpi setting is only marginally better than 1440 dpi (the Epson 1270 "resolution").

• Print quality is affected by the image editing software, which processes the pixels before sending them to the printer. Picture Window Pro   resamples the image using bicubic interpolation before sending it to the printer. Results are very sharp. Prints made with a simple Microsoft program that came with my original HP Photosmart printer were distinctly softer.

• Ink spreads when applied to paper, and it spreads differently on different papers (glossy tends to be sharper than matte). Printer software is designed to compensate for the overall tonal effects of ink spreading, but it doesn't affect resolution.

The sharp print— a preliminary criterion

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Studies on human visual acuity suggest that the smallest feature an eye can distinguish on an 8x10 inch print at 10 inches is more like 0.003 inches. At the depth of field limit, sharpness is only one third of what the eye can distinguish.

A circle, like all physical shapes, has a characteristic MTF (spatial frequency response). For a circle of diameter C, the spatial frequencies for MTF = 50%, 20% and 10% (  f₅₀ , f₂₀ and  f₁₀ ) are,

 f₅₀ = 0.72/C ;    f₂₀ = and 1/C ;    f₁₀ = 1.11/C

Would I call a print with  f₅₀ = 72 lp/in "sharp as a tack?" Hardly. It corresponds to about 40% of the achievable sharpness of an excellent 35mm camera lens. Contact prints are certainly much sharper, and the additional sharpness contributes to their clarity and luminosity. I would call  f₅₀ = 72 lp/in "pretty good" for an 8x10 inch print. 90 lp/in would be "very good." 110 lp/in would be "excellent"— "tack sharp" by any standards. These are my estimates for now, based on a comparison of prints I've made with results to be presented below; they may be adjusted in the future. If anything, they are somewhat conservative.

Of course perceived sharpness depends on print size, viewing distance and viewer expectation. The larger the print the less sharp it needs to be. A technically perfect 35mm image enlarged to 16x24 inches can look quite sharp at a normal viewing distance— about 20 inches— it can achieve the "pretty good" level, but a well done medium format or 4x5 image will blow it away on close examination. That's why people take the trouble of using big, heavy, slow view cameras.
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Printer test target

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For that reason we developed a new virtual target for printer tests that represents 1 cm (10 mm = 0.394 inch) on film. As with the previous target, spatial frequency varies from 2 to 200 lp/mm on a logarithmic scale, but the new target contains the same number of pixels as an actual scan. A typical target (reduced to fit on a web page) is illustrated below. We have chosen sharpened Provia for many of our tests because it is about as sharp as you can get with color film. Before it was discontinued, I used Kodak Supra 100 negative film for most of my work, but no MTF data was available. I'd guess it's as sharp as Provia but somewhat grainier.

1. The original target, without the effects of the film and lens, sampled at the specified rate (4000 dpi here; 2400 and 8000 dpi are also available). Anti-aliasing has been applied.
2. An area for the label and tic marks. Major tic marks (left to right) are for 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and 200 lp/mm. Minor (short) tic marks (left to right) are for 2.5, 3.5, 15, 25, 35, and 150 lp/mm. This is standard for a logarithmic scale.
3. The pattern illustrating the effects of the film and "excellent" lens. Areas where film adjacency effect or digital sharpening renders the original density, which varies between 0 and 1 (black and white), less than 0 or greater than one are displayed as 0 and 1, i.e., this image is "clipped.".
4. The target illustrating the effects of the film and lens, but this time normalized so the minimum density is 0 and the maximum is 1 (no clipping). If there is any sharpening (film adjacency effect or digital), the overall target contrast will be decreased. There are thin gray strips between sections 3, 4 and 5.
5. The target illustrating the effects of the film and lens, as in 4, but with the contrast gradually reduced until it reaches density = 0.5 (middle gray) at the top.

Results for scanned prints

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• Three targets were used: the original pattern and Provia unsharpened and sharpened. A reminder: the targets for Provia are based on simulation, and hence represent the best that can be accomplished: no camera shake (good tripod), good focus, etc. Very sharp images.
• The Epson 1270 was set for Color Ink, Photo-1440 dpi, High Quality Halftoning, Gamma = 2.2.
• The targets were printed lengthwise along the direction of paper motion, i.e., vertical in a portrait format print.
• Epson Premium Semigloss Photo paper was used.
• Images were scanned by the Epson 1640SU at its default settings. The contrast and brightness of the scanned images were adjusted for minimum and maximum densities of 0 and 100%. I used the 1600 dpi setting for magnifications of 4x and 8x; 800 dpi for higher magnifications (file sizes got enormous at 1600 dpi). At 1600 dpi, the 1640SU can resolve far more detail than the naked eye; it is more than adequate for evaluating print sharpness. Through a 10x loupe the scanned images are very nearly as sharp as the prints themselves. I didn't resize any of the targets prior to printing.
• The display images below (and also in part 4) illustrate the scanned target between 10 and 100 lp/mm (the same as the target segments illustrated above). The corresponding print density (lp/in) equals (target (film) density (lp/mm)) / magnification * 25.4 = target density * 6.35 at 4x magnification, where 10 to 100 lp/mm on the target corresponds to 63.5 to 635 lp/in on the print.
• The density plot shows 2 to 100 lp/mm (referenced to the target). There isn't much to show over 100 lp/mm (it's all aliasing). In most cases the scan illustration shows portions of bands 1 and 3 (original target on bottom and clipped, contrasty image on top).
• Assuming 75 pixels per inch screen resolution, the screen magnification (relative to print size) for these 0.5 cm = 0.197 inch target segments is 788 / (75* 0.197 * print magnification) = 53.3 / (print magnification). The scan below is greatly magnified compared to the actual 4x print: 13.3x.

Only one complete result will be illustrated here: for 4x magnification. This image is used to find the printer's ultimate sharpness. Additional images, shown in part 4, illustrate print sharpness at different magnifications.
 

Print magnification: 4x Illustrates ultimate printer sharpness 4000 dpi scan; 1000 dpi sent to printer Screen magnification @ 75 pixels per inch: 13.3  Note the missing tic marks! It might be wise to resize this image down (to 500 dpi or below) before printing (practically speaking, this is almost never a problem). A small amount of color fringing is visible around some of the edges. These colors are barely visible to the naked eye, but they show up quite clearly under a 10x loupe.  The ultimate printer sharpness can be derived from the density curves at 4x magnification. For the original target,  f50 and f10 are 120 and 190 lp/in on the print (19 and 30 lp/mm referenced to the film). For the sharpened Provia, f50 and  f10 are 165 and 190 lp/in on the print (26 and 30 lp/mm referenced to the film). Response above 190 lp/in is mostly aliasing— garbage. Sharpening improves the image resolution, even at low magnifications. The effects of sharpening, which boosts MTF at high spatial frequencies, are illustrated below. These density curves may look ugly, but the 1270 is an outstanding printer capable of making extremely sharp images. These results are extremely sensitive; they reveal the finest details of printer performance. f50 = 120 lp/in is impressive performance.

More of these images are in part 4 .

How many image pixels per inch (ppi) do you need to send to the printer?

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300 dpi is sufficient for excellent sharpness for all magnifications, even in small prints. There is little improvement beyond 300 dpi. Results are still very good at 250 dpi. For large prints intended to be viewed at a distance, you can get by with well under 250 dpi.

Below about 200 ppi, print resolution is beneath the capabilities of the 1270 printer; it's pretty much based on the original image. For a sharp image,  f₅₀ is roughly 0.4*ppi. Sharpening always improves things somewhat. Large prints at 150 dpi, for example a 2400 dpi scan from 35mm film printed at 16x (16x24 inches), have adequate sharpness for their size, even though they don't quite meet the "pretty good" standard for small prints (that would require a 4000 dpi scanner). They won't come close to good scans from medium and large format film, but if they're sharp to begin with, they won't look bad either.

If your image is soft to begin with, you won't benefit from the full 300 dpi. If I'm scanning 35mm film and I don't plan to print larger than 8x10, I usually set my Canoscan FS4000US scanner to 2000 dpi (the next step below its maximum of 4000 dpi). This speeds things up a lot and I can still print at 250 dpi— sufficient for all but the most insanely critical applications.

Resizing the image to a higher resoluton generally does very  little to improve printer sharpness— you are limited by the information in the original file. Resizing with sharpening might help a little, but don't expect much. Remember, the image editor resizes the image— transparently to the user— when it sends it to the printer. You never need to worry about the exact correspondence between the ppi of your print and the dpi "resolution" of the printer.
 

Now let's look at sharpness for a film image (simulated, so it indicates what you'd get under ideal conditions).

 Summary

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• Based on the original target printed at 4x magnification, the Epson Photo Stylus 1270 has a resolution limit of about 120 lp/in at the 50% contrast level and 190 lp/in at the 10% level— extremely sharp; perhaps as good as the naked eye can see at reasonable viewing distances. Epson's specified "resolution" of 1440 dpi is merely the maximum dot density— the spacing of the stepper motor. Most of the time print sharpness is usually limited by the image and the scanner rather than the printer.
• The 1270's perceived sharpness ( blue; most related to the 50% MTF level) and resolution ( red; most related to the 10% MTF level) are summarized in the curve on the right for sharpened Provia, which is about as sharp as color films get. The margin of error is about ±4% at the 50% MTF level and ±10% at the 10% level.
• The resolution at the 50% level for the sharpened Provia is greater than the printer's resolution with the original target because sharpening reduces low frequency components relative to high frequencies. The ultimate resolution (closer to the 10% level) is relatively unaffected. Details are illustrated in part 4.
• Sharpening always improves perceived print sharpness. It compensates for some of the MTF rolloff in the film, lens and printer. It should be performed whenever possible. But care must be taken to prevent smooth areas from skies from becoming grainy. This is done through the use masks and thresholds in unsharp mask.
• The advantage of medium format is that it only requires about 1/2 to 2/3 the magnification of 35mm. Big advantage! But 4000 dpi scanners for medium format are very expensive: over $2,500. Very nice if you can afford one.
• This could be a good starting point for an industry standard for printer sharpness, though consumer interest might be limited. The 1270 is extremely sharp as it is; a sharper printer wouldn't appear much better to the naked eye.
• A 2400 dpi scan can look very good at 8x and pretty good at 12x magnification, but a 4000 dpi scan has an advantage, even at 8x. I discuss scanners in Making fine prints. I now use a Canon FS4000US CanoScan for most of my 35mm work (except for panoramic images). Inexpensive 2400 dpi flatbed scanners don't seem to have as good resolution as 2400 dpi dedicated film scanners.

How the results are obtained The printer test targets are created by the Matlab program, MTFcurve.m , which you can download on your computer and run if you have Matlab installed (I have version 5.3). It is run exactly as described in Part 2 , except that the first argument, the 50% MTF frequency of the lens, is entered as a negative number. Here are two examples. Comments follow the %-sign. mtfcurve -45 13 61 2 2400/25.4         % Velvia, excellent lens, 2400 dpi, unsharpened. mtfcurve -40   0 61 2 4000/25.4 .37   % Provia, excellent lens, 4000 dpi, sharpened with ksharp = 0.37 Portions of two targets are illustrated below actual size— 1 screen pixel per target pixel— for 10 to 100 lp/mm, the region of greatest interest. These segments represent 788/1575 cm = 0.5 cm (0.197 inch): half the original 4000 dpi target, which varies from 2 to 200 lp/mm. The 50% and 10% MTF points for Provia with the excellent lens sharpened with ksharp = 0.37 (the upper pattern in the upper image, below) are 57.4 and 82.5 lp/mm. The 50% and 10% MTF points without sharpening (the upper pattern in the lower image, below) are 26.8 and 55.3 lp/mm. The sharpened plot has outstanding resolution— close to the ideal target for the 4000 dpi scan— because the maximum sharpening boost takes place at 78 lp/mm— half the sampling frequency. From these images it appears that the 10% MTF point provides a reasonable estimate of the limit of visible resolution. The 50% MTF point is more associated with perceived sharpness. Download the targets Targets can be downloaded by right-clicking on the appropriate file name in the table below. All contain text labels. They have been rotated 90 degrees from the normal orientation (above) for optimum TIFF data compression.    Description Scan dpi File name Size kB Velvia unsharpened 2400 Print_Velvia2400nosh.tif 76 Velvia unsharpened 4000 Print_Velvia4000nosh.tif 201 Velvia sharpened (ksharp = 0.22) 2400 Print_Velvia2400sh22.tif 79 Velvia sharpened (ksharp = 0.28) 4000 Print_Velvia4000sh28.tif 206 Provia unsharpened 2400 Print_Provia2400nosh.tif 75 Provia unsharpened 4000 Print_Provia4000nosh.tif 200 Provia unsharpened 8000 Print_Provia8000nosh.tif 481 Provia sharpened (ksharp = 0.29) 2400 Print_Provia2400sh29.tif 82 Provia sharpened (ksharp = 0.37) 4000 Print_Provia4000sh37.tif 210 Using the targets The first thing you'll want to do once you've saved a target is to load it into your image editing program is to rotate it 90 degrees and have a close look at it at 1:1 or larger magnification. You may want to sharpen it to see how real sharpening compares to the computer model (they should be very similar with Radius = 1). You can rotate or resize it, but you should be aware that rotation by angles other than ±90 or 180 degrees and resizing invoke an anti-aliasing algorithm that may soften the image slightly. You can change the target color to C, Y, M, etc. If you make changes, be sure to save them with different file names so you don't lose the original.  Now you are ready to print the target. You may want to print the original version before you try the modified versions. The narrowest print the Epson 1270 can handle is 3 inches wide. I cut 8.5 x11 inch (letter sized) paper into 4.25 x11 and 3.5x8.5 inch strips for the tests. The larger size is used only for magnifications between 18 and 26 (as high as I need to go).  The print magnification is equal to the length of the image in cm. I made prints at magnifications of 4, 8, 12, and 16x (4 cm, etc.). Each magnification has different attributes: at 4x sharpness is entirely limited by the printer; at 16x it is limited by the target. 8x and 12x represent typical magnifications for letter (8.5½x11 in) and A3 images (11.7x16.5 in) from 35mm, respectively.  You can learn a lot by studying the prints with the naked eye and under a loupe. But if you have a high resolution scanner, you can take the analysis much further.  The prints were scanned on the 1600 dpi Epson 1640SU Photo scanner, which is a flatbed hybrid that can also scan film. (A cheap 300 dpi optical resolution scanner won't do.) I used the 1600 dpi setting for magnifications of 4x and 8 x; 800 dpi for higher magnifications (file sizes got enormous at 1600 dpi). At 1600 dpi, the 1640SU can resolve far more detail than the naked eye; it is more than adequate for evaluating print sharpness. Through a 10x loupe the scanned images are very nearly as sharp as the prints themselves. I didn't resize any of the targets prior to printing. Analysis of targets and scans I've written a Matlab program, MTFscan.m , that plots print density as a function of spatial frequency for the 10 mm target. You can download it by shift-clicking here . Matlab must be installed to run it. I have version 5.3. A $99 student version is available at campus bookstores. If you're reading this, you must be a student (of sorts). You can also use a public domain program, ImageJ, for the analysis. It works very nicely— all it lacks is a proper logarithmic x-axis scale, but it can be easily computed. Typical MTFscan outputs are illustrated on the right for targets (not yet for scanned prints, which will be tackled shortly).  The first image is the the density vs. spatial frequency for the original pattern without the effects of film or lens; band 1 of the above target and the lower part of the above segments. The rolloff is due to the sinc3 sensitivity of the film scanner, discussed in part 2 , which is necessary for anti-aliasing. At 4000 dpi = 157.5 dpmm, response above 78.7 lp/mm (the Nyquist frequency) consists of aliasing— artificial low frequencies and displaced edges. I use the red sine curve on the bottom when I zoom in on Matlab plots to check for aliasing. Because the response of the scanned prints contains large irregularities at high spatial frequencies, I visually estimate the 50% and 10% MTF frequencies ( f50 and  f10 ) from the plots. These estimates have about a ±4% margin of error for  f50 and ±10% for  f10 , where more irregularities are visible.. The 50% frequency is associated with perceived image sharpness; the 10% MTF frequency is associated with perceived lp/mm resolution. See part 1 .  For the original pattern (above right), f50 and  f10 are 65 and 110 lp/mm.  The upper plot in the figure to the right is the density vs. spatial frequency for Provia with the excellent lens scanned at 4000 dpi, unsharpened. The 50% and 10% MTF frequencies are 32 and 61 lp/mm.  The lower plot is for Provia sharpened with ksharp = 0.37 (radius = 1); band 4 of the above target. The characteristic sharpening at contrast boundaries and high frequency boost is apparent. Because this boost tends to get lost in prints and contrast is adjusted accordingly when prints are made, we reference  f50 and f10 to the steady-state low frequency response, which is about 0.63, since this plot is normalized to 1 at the maximum.  f50 and  f10 are 62 and 85 lp/mm, much higher than the unsharpened image. Later we will look at similar plots for scanned prints. These plots are similar, though not precisely identical, to MTF plots. The difference is that the input target to an MTF plot must be sinusoidal. I used steps (derived from a sine function) because they provide more visual information about image sharpness. At high spatial frequencies, where the response becomes sinusoidal, these plots are identical to MTF.   Mixed units  I use familiar units for describing resolution. For better or worse that means using line pairs per mm on film and targets and line pairs per inch on prints. It gets confusing— I had to correct several errors. On the other hand, using less familiar units would also be confusing. Mixing units in this way is not without its perils. It lead to the crash of the $125 million Mars Orbiter on September 23, 1999. Running MTFscan MTFscan.m and Matlab must be on your computer. The scanned target should be horizontally aligned so that spatial frequency increases from left to right. Rotate 90 degrees in your image editor if necessary. Recall that rotations by other than ±90 or 180 degrees invoke an anti-aliasing routine that may reduce sharpness. Carefully crop the left and right of the scanned target at the centers of the 2 and 200 lp/mm tic marks (the extreme left and right of the target). I adjust the brightness and contrast (using Picture Window's Levels and Color... transformation) so the minimum and maximum densities are 0 and 100%. Save the cropped image in a standard file format and extension, preferably tif. Matlab also supports bmp, png, and jpg. Run MTFscan with the command,  mtfscan filename.ext    % (ext is typically tif) The image will be displayed along with axes that indicate the x and y-coordinates. Enter the y-coordinates of the first pattern to scan. Enter the y-coordinates of the second pattern to scan; none if only one plot is desired. Enter the print magnification; 1 for an original target. It's a good idea to add labels to the plots, e.g., "Original target," "Provia unsharpened," etc.

Images and text copyright © 2000-2013 by Norman Koren. Norman Koren lives in Boulder, Colorado, where he worked in developing magnetic recording technology for high capacity data storage systems until 2001. Since 2003 most of his time has been devoted to the development of Imatest. He has been involved with photography since 1964.