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

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Table of contents

for the
image sharpness

Part 1: Introduction
Part 1A: Film and lenses
Part 2: Scanners and sharpening
Part 3: Printers and prints
Printer / print sharpness
Printer test target
Analysis of targets and scans
Results for scanned prints
Part 4: Epson 1270 results
Part 5: Lens testing
Part 6: Depth of field and diffraction
Digital cameras vs. film, part 1 | part 2
Part 8: Grain and sharpness: comparisons
4000 vs. 8000 dpi scans
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Note (November 2004): This page is out of date; it hasn't been updated for my Epson 2200 printer and my (superior) Epson 3200 scanner.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.
Imatest: affordable software for measuring sharpness and image quality

Related pages:  Photo printers | Pixels, images, and files

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.

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 maligned and 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.

Printer / print sharpness

Now that we've discussed sharpness and MTF in film, lenses, scanners and sharpening algorithms, a few questions remain. The answers must be determined experimentally because there are no convenient mathematical equations for characterizing printers. There are several reasons. The only way to determine a printer's sharpness capability, which includes the effects of software, ink and paper, is to make test prints over a practical range of magnifications.

The sharp print— a preliminary criterion

In my research for the Depth of field page I learned about a criterion for print sharpness that was used to design the depth of field scales on lenses with focusing mounts back in the 1930's. The smallest distinguishable feature on an 8x10 inch print viewed at a distance of about 10 inches was assumed to be 0.01 inch. When a pinpoint image is misfocused, it becomes a circle known as the circle of confusion. Depth of field scales are set for a 0.01 inch circle of confusion on an 8x10 inch enlargement (0.032mm on 35mm film to be enlarged 8x).

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
f50 is familiar from film, lenses and scanners.  f20 is interesting because it is the inverse of C. For C = 0.01 inch,  f50 = 72 line pairs per inch (lp/in); f20 = 100 lp/in;   f10 = 111 lp/in. We use f50  as a standard of comparison since it is most closely correlated with perceived sharpness.

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

The 0.5 mm target used in Parts 1 and 2 is too small for printer tests; it was designed to illustrate film image sharpness on a video monitor. It contains several pixels per scanned pixel, and as such it doesn't represent an actual pixel-for-pixel scan. At 10x print magnification the length of the print would only 0.5 cm (0.197 inches).

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.

GIF image of 4000 dpi Velvia unsharpened 10 mm target, NOT the actual target
This 750 pixel wide GIF image is not the actual 1575 pixel wide target, which is a downloadable TIFF file. Some Moiré fringing due to interaction between the pattern and screen pixels is visible and unavoidable. The target is divided into five zones. From bottom to top they are,
  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.
Targets are available representing Provia and Velvia films with the "excellent" lens scanned at 2400 and 4000 dpi, with and without sharpening. There is also a target for Provia unsharpened at 8000 dpi. You can learn how to download and use them in How the result are obtained, below. The Nyquist frequency— the frequency beyond which response is a form of garbage called aliasing, is 47.2 lp/mm for 2400 dpi scans and 78.7 lp/mm for 4000 dpi scans (half the scan dpmm). Some anti-aliasing is applied to the original pattern below the Nyquist frequency to minimize interference between the pattern and the sampling rate. This represents actual scanner performance and sets limits on print sharpness at large magnifications.

Results for scanned prints

The targets were printed at magnifications of 4x, 8x, 12x and 16x, then scanned with the Epson 1640SU. Except as noted (in purple in the tables below), prints were made and scanned under the following conditions. The scanned prints were analyzed for MTF using Mtfscan.m. Because the response of the scanned prints contains large irregularities at high spatial frequencies, I visually estimated the 50% and 10% MTF frequencies ( f50 and  f10 ) from the Mtfscan plots. Details below.

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?

There is no one-size-fits-all answer, but the table below gives a strong indication of what to expect. Remember, the total image pixel size and print size are what you use for this calculation. You may be confused by an image size specified as 8x10 inches at 250 ppi. The actual image is 2000x2500 pixels— you can print it any size you want.

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.

Print sharpness for the original target
for the Epson 1270 set at highest print quality
Test ( unless noted,
4000 dpi scan,
Print magnifica-
tion / pixels per
inch to printer
 f50 lp/mm
 ref. film
 f10 lp/mm
 ref. film
 f50 lp/in
 f10 lp/in
Original target (target) 65 110 n/a n/a  
Provia unsharpened (target) 32 61 n/a n/a For comparison
with original target.
Provia sharpened 0.37 (target) 62 85 n/a n/a Sharpening brings  f50
close to original target.
Original target 4x 4x / 1000 19 30 120 190 4x prints reflect ultimate
printer resolution.
Original target rotated 90o
(direction of print head)
4x /1000 17 27 108 171 About 10% lower resolution
than the standard direction.
Original target 
Matte Heavyweight
4x /1000 18 27 114 171 Very close to Semigloss;
better than expected.
Original target 8x 8x / 500 35 50 111 158  Excellent
Original target 12x 12x / 333 50 65 106 137  Excellent
Original target 16x 16x / 250 54 70 86 111  Very good

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

Print sharpness for Provia film
for the Epson 1270 set at highest print quality
Test ( unless noted,
4000 dpi scan,
Print magnifica-
tion / pixels per
inch to printer
 f50 lp/mm
 ref. film
 f10 lp/mm
 ref. film
 f50 lp/in
 f10 lp/in
Provia unsharpened (target) 32 61 n/a n/a  
Provia sharpened 0.37 (target) 62 85 n/a n/a  Close to original target.
Provia sharpened 0.37 4x / 1000 26 30 165 190 Shows improvement from
sharpening, even at low 
Provia sharpened 0.37 
rotated 90o
4x / 1000 19 27 120 171  " "
Provia sharpened 0.37 
Matte Heavyweight
4x / 1000 18 29 114 184  
Provia unsharpened 8x / 500 24 40 76 127  
Provia sharpened 0.37 8x / 500 41 52 130 165  
Provia sharpened 0.37 
2400 dpi scan
8x / 300 31 41 98 130  
Provia unsharpened 12x / 333 27 45 57 95 Needs sharpening!
Provia sharpened 0.37 12x / 333 46 56 97 118 Still very sharp.
Provia sharpened 0.37 
2400 dpi scan
12x / 200 35 43 74 91 Reasonably sharp; 76% 
of 4000 dpi scan.
Provia sharpened 0.37 16x / 250 51 66 81 104 Very large; still OK.


 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.
Section of target, full-sized (1 screen pixel/image pixel)

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.

Part 4: Epson 1270 test results

Images and text copyright © 2000-2014 by Norman Koren.
Norman Koren lives in Boulder, Colorado, founded Imatest LLC in 2004, previously worked on magnetic recording technology. He has been involved with photography since 1964.