DPI vs. PPI
The question is sometimes asked, "What is meant by dots per inch compared with pixels per inch?"
Printer DPI and PPI, General
Scanner DPI/PPI
Image File PPI
Horizontal/Vertical DPI
Monitor/Display PPI/DPI
LPI (Lines Per Inch)
Laser Printers
Inkjet Printers
Printer DPI and PPI Ratings, General
Dots per inch stands for the maximum number of tiny spots of ink that the printer can place in a straight line where the spots are theoretically small enough (i.e. ignoring spreading or smearing effects of ink on paper) that if placed in every other such dot position leaving white space between them, the spots can be individually distinguished.
Pixels per inch stands for the maximum number of unique positions in a straight line that the printer can place an ink spot under control from the outside world, namely from a computer connected to the printer.
Lines per inch stands for how close thin parallel lines can be printed and still be distinguished in the finished printout. The spaces between the lines count as "lines".
Pixels per inch and dots per inch originally referred to the same thing. The printer mechanism was under the direct control of the computer and was physically positioned and placed dots as directed by the computer. Back then, most printer mechanisms were limited to placing dots only in positions suggested by a grid of dots X per inch horizontally and Y per inch vertically, for example 100x100 dpi
Nowadays, many printers put dots "wherever they want" as opposed to in positions suggestive of a horizontal/vertical grid. Still there is a minimum dot size and a minimum dot spacing.
A picture file (image file) represents pixels in a uniform horizontal/vertical grid pattern. And the printer needs to make a finished picture of the size, say 5x7 inches, that the user chose regardless of the number of pixels in the picture file. To simplify the process of relating the pixel count in the picture file to the possibly non-uniformly spaced dots on the paper, the printer or its supporting software may generate a temporary intermediate picture file with a set number of pixels per inch. The printer may have, internally, several choices of ratio of pixels to dots and the published rating can be the largest ratio except that the published rating may not exceed the dpi rating. Therefore there might be three "per inch" values involved at a given time, the pixels of the original picture file, the pixels per inch that the printer works with, and the dots per inch of the printer mechanism.
Pixels per inch is usually not mentioned with printers. All printers come with their own software (including parts called drivers) to install on your computer. Usually the software does not let you exercise control over individual dots using your picture file. Rather the printer takes your picture file or data file and uses its own built in logic to lay down the dots and create the printed output. We are led to believe that a printer's ppi is usually a fraction such as a half or a third of its dpi rating.
When a temporary picture file is created, there are at least two levels of software in use. High level software (which may run in your computer) takes your picture file and creates the temporary file. Low level software runs in the printer, takes the temporary file and controls the dot size and dot placement on the paper.
Sometimes a printer is advertised using a phrase such as "300 dpi 1200 dpi quality". This means that the printer has some way of making dark edges on a light background appear smoother than the first number would otherwise suggest. A printer with 300 dpi 1200 dpi quality definitely cannot resolve alternating dark and light pixels less than 1/300'th inch each. But curved and diagonal lines and color boundaries should not have jagged edges suggesting individual dots rigidly positioned on a grid with a 1/300'th inch pitch.
Color Shading; Gray Scale; Dithering
A simple printer (with black ink only) can only produce two "colors": black where ink is deposited, and white where nothing is deposited. Shades of gray are achieved by producing spots of different sizes and/or different spacings. Often dots are printed only at the spacing implied by the dpi rating, with white space in between..
Similarly, with few exceptions, color printers can make spots of only a small number of different sizes. The different permutations of spot size for each of the four colors magenta, cyan, yellow, and black come nowhere near the 16 million or so colors that the printer is supposedly capable of producing.
The printer typically uses multiple dot positions, often as clusters of say 2x2 dots or 3x3 dots, each individual dot with a different color to create a solid color patch that at a distance appears as the desired color. In most cases the ink or toner spreads or smears enough so a pattern of 2x2 or 3x3, etc. "macroblocks" cannot be identified. Also the better printers do not break up the printable area into macroblocks (dot clusters) at first when assembling the picture file data but rather vary the color of each individual dot position more randomly. Color printers achieve a more random less regimented appearance of their output simply because the individual magenta, yellow, etc. dots may or may not overlap.
Juxtaposing small spots of different colors to achieve shades of color not otherwise achievable (using the colors of ink provided) is called "dithering". Some printers may break up a dot grid into specific 2x2, 3x3, etc. clusters but may require more dithering, namely using adjacent clusters of differing shades, to achieve all desired color shades.
Picture File Pixels per Inch
Pixels per inch is not relevant until you are ready to print the picture file or data file.
If you have a file with so many pixels across and you want a finished print so many inches across, the pixels per inch relative to the file is dictated. But the printer still prints at its own dpi, or in some cases its own ppi that may be a fraction of its dpi rating. The printer (or the computer) will "scale" the picture file, often producing a temporary picture file with the exact number of pixels across to go with the dpi rating of the print mechanism. If the printer works with more pixels per inch than the picture file has, the printer duplicates rows of pixels from the original picture file when it makes a temporary picture file. If the printer has fewer pixels per inch than the finished picture should have, then the printer drops rows of pixels from theoriginal file here and there. The better printers' processing does some blending with adjacent rows as opposed to omit rows entirely.
The typical user will crop pictures in different ways while printing them all at roughly the same finished size. Each picture file then has different horizontal and vertical pixel counts. The scaling process is automatic so the user should not have to worry about printer dpi versus picture file ppi.
It is customary to describe the resolution of a picture file using the total numbers of pixels horizontally and vertically.
One to One Pixel Matching
Problems can occur when the pixels per inch for the desired print size coincidentally comes out close to but not equal to the ppi for the printer. In this case it is not unusual to get repeating streaks or moire patterns. If the file ppi and the printer ppi can be made equal (one to one pixel matching) the print comes out very smooth.
Meanwhile many printers do not allow you to, or at least do not allow you to easily, match the pixels in your file with the pixels the printer works with.
Getting this to match requires either cropping the picture just right or adjusting the finished print size just right. This is usually a trial and error process and most users do not bother. It is difficult to second guess what the printer's internal scaling process does.
If the printer uses a regimented cluster pattern or otherwise has a dot pitch, having the pixel spacing close to the dot pitch can also result in undesirable moire patterns.
Scanner DPI Ratings
For a scanner, dots per inch equals pixels per inch. The term "samples per inch", or spi, is also used to describe scanner resolution. One "sample" equals one pixel or one dot. The process of converting analog material to digital, for example storing a printed picture as a data file for later reproduction, is also called sampling. In the case of the picture, one literally takes "a sample here, a sample there" over the surface area of the original picture, where the more tiny "dot" samples are gathered, the more accurate a copy of the picture can be recreated from the data file.
The scanner sensor bar, like the printer print head, has a fixed number of pixel positions per inch. Also, the sensor, as it moved down the paper, has a fixed number of steps per inch (or perhaps a choice of a small finite number of step sizes). So, given the dimensions of the area being scanned, the numbers of pixels horizontal and vertically in the picture file is predetermined. After the picture file is generated, it is not meaningful to discuss ppi or dpi until a print is going to be made and its dimensions are selected.
You can choose to scan at lesser resolutions than the scanner is capable of in order to end up with smaller (more manageable) picture files or to make the scanner work faster. To achieve a faster scan, the scanner might capture, say, every other pixel position in the sensor and move the sensor down the page using steps twice as large (for scanning at, say, half the dpi rating) Different scanners use different processings, for example one scanner may scan at the maximum dpi rating all the time. For lesser resolution scans it digests the resulting picture file, usually blending adjacent pixels before dropping any, to get the file down to the user chosen resolution and size.
Monitor and Projector DPI Ratings
Normally the resolution of computer monitors, TV sets, and video projectors is not discussed using dpi or ppi. Rather the total pixel counts horizontally and vertically are used. It is quite obvious that if "the same picture" is shown with the same level of detail on two monitors of different sizes (in inches), the respective dpi ratings must differ. Meanwhile the resolution of picture detail can be different for monitors of the same size depending on the quality of the electronics and display elements inside.
Dot pitch of cathode ray tubes (which does imply a dpi rating) is unrelated to pixel size. Dot pitch is a physical characteristic of the CRT while pixel size is governed by the subject matter being displayed at the time. Dot pitch is usually smaller near the middle of a CRT screen and larger near the sides. Dot pitch of LCD screens and LCD and DLP(tm) panels equals the pixel size.
Horizontal and Vertical DPI Ratings May Differ
This is not unusual for printers and scanners. For example the dpi may be rated as "1200 x 600". If you print a picture file intended to be printed with horizontal and vertical pixels per inch ratings the same on a printer whose horizontal and vertical dpi ratings differ, the picture still comes out right. The printer or its drivers in your computer automatically produce a temporary file with the proper horizontal scaling and the proper vertical scaling.
Most digital (still) cameras produce picture files intended to be printed with the same horizontal and vertical pixel count but many video cameras do not. Should you wish to print a picture file intended to be printed with differing horizontal and vertical ppi counts, you would need to do intermediate processing on your own to stretch (or morph) the picture prior to printing. Sometimes such stretching software is provided by the printer manufacturer.
Scanners normally yield picture files representing equal horizontal and vertical ppi counts even if the horizontal and vertical dpi ratings for the mechanism are different. This way, if you scan a picture and immediately print it, the picture comes out proportioned "right" regardless of the dpi ratings of the scanner and printer. There may be a choice of obtaining scanned images in a "raw" form where the file reflects the actual scanned dots per inch even if horizontal and vertical dpi differed.
For monitors, having different horizontal and vertical dpi is common. The term used here is "non-square pixels". CRT monitors can usually be adjusted optically (using knobs) to make the pixels square regardless of horizontal and vertical pixel count of the source material.
More On Lines Per Inch (LPI)
Resolving of picture file picture detail in the finished output is often stated in terms of "lines of resolution". Technically, a reference distance, such as "the height of the screen" or "one millimeter" must be included. For printers, one inch is a common reference distance. Lines of resolution is typically measured by observing how close parallel lines (or dots in a row) can be spaced and still be distinguished. (The white spaces between "lines" also count as lines except as discussed by traditional photographers; the latter folks are becoming used to referring to one black line and the white space next to it as a "line pair".)
For printers that use a rigid grid pattern for dot placement, it is not unusual to compute an lpi rating as one divided by the observed dot pitch although only the black dots should be taken into account for a color printer.
Since different kinds of inks behave differently on different kinds of paper, the resolution of picture detail from a given printer can be seen to vary. It would be necessary to issue a separate lpi rating for each ink/paper combination if one does not want to simply use the results from the best combination which is the accepted rating.
The term "lines of resolution" has been around for a long time to refer to resolving of picture detail even if a test pattern used small dots instead of parallel lines. Therefore the term "dpi" can be reserved for describing the manner in which the printer mechanism works and "lpi" can be reserved for describing the appearance of the printed output.
Scanners and LPI
The material being scanned may have a resolution up to so many lines per inch. Two hundred lpi is considered excellent for ordinary glossy photographic prints. Because fine picture details may land between the scanner sensor pixels, it takes a higher scanner dpi to preserve a given lpi of the original. Scanning at a dpi twice the desired lpi will always capture detail at said lpi. But viewing tests have shown that on average, scanning at a dpi 1.4 times the desired lpi produced results that are hard to distinguish from scanning at twice the desired lpi. The reciprocal, approximately 0.7 (scanning at X dpi captures 0.7X source lpi) is called a Kell factor. It is subjective. A more quick and easy calculation is had by using a Kell factor of 0.67 (two thirds); scan at 300 dpi to preserve 200 lpi of source detail. For important or archival digital storage of material where the resulting larger file sizes can be handled and managed, scan at a dpi that is fully twice the lpi of the source.
Laser Printer DPI Ratings
Many laser printers have a dot grid that would suggest pixels per inch but usually the grid pattern is on a diagonal rather than being horizontal/vertical.
We magnified some samples from a number of "600 dpi" color laser printers and also one "1200 dpi" model and found that for printing photographs there was a fundamental dot spacing or "dot pitch" for each color of roughly 1/150'th of an inch as opposed to 1/600'th. This is enough to explain why the printouts appeared grainy compared with (chemical) photographic prints and photo quality inkjet printer output. So we expected that while the laser printer might be able to put spots in 600 unique positions per inch, the spots might not necessarily be of a specific or desired color. Typically the color printer has separate dot grids for each of the four colors (magenta, yellow, cyan, black) with each grid oriented at a different angle.
We are not sure which printers build a temporary picture file with a pixel per inch rating a fraction of the advertised 600 etc. dpi rating versus build a temporary file with a ppi rating equal to the dpi rating versus work directly from the user supplied file. Since separate sub-images for magenta, cyan, etc. would need to be built if temporary files are used, using the full dpi rating is more likely to run into insufficient memory problems.
Given a 600 dpi printer using a grid pattern with a 150 dpi dot pitch, 4x4 dot clusters are implied for dithering purposes. Sixteen levels of color intensity plus white can be achieved, namely with one to all 16 dots in the cluster filled (or all empty). Some additional levels of intensity could be achieved if the toner density within a dot could be varied or if two or more consecutive dots could hold toner more densely than individual dots. The appearance of the output suggested that rather than put individual dots into positions within a 1/150'th inch or so cluster, the printer made a more or less round spot whose size seemed to vary in an analog manner.
To achieve lighter color shades, the toner dots themselves were on the order of 1/600'th of an inch in size. Perhaps this is where the 600x600 dpi (horizontal and vertical) rating came from. If there are four colors, each with an implied grid with 1/150'th inch dot pitch, we cannot say that four times 150 equals 600 dots per inch. Any given 1/150'th inch square might have one spot of each color. If the spots happen to be evenly spaced in a row then the next row is 1/150'th inch away. Or in another location in the picture they are arranged in a square in which case they represent rows 1/300'th inch apart and columns 1/300'th inch apart.
Even for darker colors most of the laser printers we examined put one large spot instead of several small spots into each grid position. With one black spot per 1/150'th inch grid position, the lpi rating of the printer could be no more than 150. A ppi rating of more than 150 would then not be useful.
Halftoning is a good description of the way the image (or color subimages) are formed by a typical laser printer. Halftoning is the breaking up of a photograph into tiny uniformly spaced dots which is how traditional printing presses printed photographs. Taking just one primary color (and one dot structure) at a time, for a light shade we see uniform rows of dots (or stripes) of color on a white background. As the color gets deeper, the dots get larger and smear into one another. Eventually the magnified view shows uniform rows of white dots on a colored matrix-like or screen-like background and finally solid color. (The last of the white space to be filled with color is the middle of each foursome of dots in the grid pattern.) Generally the smaller dots of different primary colors do not land atop one another. While for video, dithering per se means adjacent pixels of nearly the same color, what is actually seen in the magnified laser printer output is adjacent color spots of widely varying colors, and also tiny scattered areas of white space, all still blending to the desired color shade when viewed from not so close up.
We did notice that dark text appeared crisper (with straighter edges) than the 1/150'th inch or so dot spacing would otherwise suggest. Perhaps this crispness is limited to line art and also text using fonts pre-loaded into the printer's memory, as opposed to photographic images. All laser printers generate a pattern of electrical charges on a drum or flat belt to form the image. We believe that for a 600 dpi printer the charge pattern can be made sharp enough to suggest 600 dpi but the dot spacing has to be greater so the toner can be spread thin enough for light shades of color. Perhaps for dark colors the portion of the larger dots (toner clumps) extending past the edge of the charged pattern does not adhere so a crisp edge is obtained. Lighter (e.g. gray) text did not appear as crisp.
Also it should be noted that the human eye only recognizes fine detail in terms of light versus dark, not "light" versus "slightly lighter" or "dark" versus "not quite so dark". So where a dark area meets a light area, imperfect dithering on each side of the boundary won't be noticed.
Meanwhile it is not correct to say that using a grid with a dot pitch of 1/150'th inch can reproduce 300 lines of resolution simply because some of the time the dots will be small enough that white spaces surround each of them. A dark picture detail might happen to be where the printer is unable to deposit a spot of ink.
One color laser printer (from Brother) did not have a visible grid pattern but the dot spacing tended to average out at the same 1/150'th inch for light colors and closer for dark colors. While we thought that the more random appearing dot placement would give a smoother picture, photographs looked more "grain" compared with output from some printers that did have a grid pattern.
Another color laser printer (a Dell) had parallel lines rather than dots. (The lines are thicker for deep color and thinner for lighter shades.) The lines for each primary color (cyan, yellow, etc.) run at different angles across the paper.
The end result is that the dot positions on the paper do not naturally correspond to the pixels per inch of the picture file. The printer software translates the picture file contents to generate the color subimages using the diagonally oriented printer grid patterns. In addition, the (diagonal) tilt of the grid patterns make it all but impossible to achieve a one to one match between picture file pixels and printer dots.
Higher resolution (a higher lpi and being able to handle a larger ppi) could have been achieved by putting two or more small dots instead of one large dot in each of those (1/150'th or so) inch grid positions where fine detail needed to be reproduced. This would result in color inaccuracy at those locations, given smaller regions to perform dithering in. But where there is a lot of fine dark/light detail, the human eye is less likely to notice color inaccuracy. None of the printers we examined work this way.
Above are some laser printer samples, all at the same magnification. The left sample shows the halftone dot pitch of about 1/150'th inch. To the left is a lighter color patch and magenta and cyan dots can be seen in their respective grid patterns. To the right is a deeper color patch with magenta more or less covering the area with small cyan dots. This is a common technology, used by Hewlett Packard, Lexmark, and Samsung.
The center sample shows a criss crossing stripe pattern used instead of a dot pattern. The stripes are about 1/200'th inch apart. Yellow stripes are nearly vertical; magenta stripes slope up to the right. A Dell 1320C printer provided this sample.
The right samples show a somewhat random toner grain distribution instead of a halftone pattern. The samples show the change in toner spot spacing for color patches of differing shades. The source includes a heavy black line running horizontally to exemplify how crisp a deep color to white boundary can be made. These samples are from a Brother MFC 9040 printer.
Other samples of halftoned color photographs for comparison:
A magazine cover: 1/200'th inch dot pitch for each color subimage
A color photocopy: 1/180'th inch
A magazine page: 1/170'th inch
A glossy newspaper advertisement: 1/150'th inch
An ordinary paper picture ad: 1/130'th inch
(The above are not intended to be representative; for example not all photocopiers use a 1/180'th inch dot pitch.)
We could conclude that the typical consumer grade color laser printer (600 dpi) produces images comparable to those in advertising circulars found in the Sunday paper and not quite as good as magazine photographs.
Some actual dot pitches:
HP CM1312 and CP1518 -- 165 horizontal, 150 vertical*
Samsung CLP 315 and CLX3175 -- 135 x 135
Lexmark C540N and C543N -- 165 x 150
Xerox Duplicolor 12 (copier) -- 190 x 190
Dell 1320c (line pitch) -- About 165 for colors, 185 for black.
* None are perfectly horizontal/vertical
Inkjet Printer DPI Ratings
A typical inkjet print head has a column of nozzles, sometimes zigzagged or staggered to permit a closer vertical spacing. The vertical spacing represents the vertical dpi rating.
A typical inkjet printer varies the dot spacing horizontally to achieve darker or lighter shades of color. (The frequency of droplet emission is varied as the print head sweeps across the paper at constant speed.) DPI refers to the minimum spacing. The term "dot pitch" would then not be used. This means that the horizontal dpi realized does not correspond directly to the ppi computed for the picture file after the picture size is selected. The better quality printers can also vary the droplet size but are usually limited to a small number of different sizes.
The printer's internal processing still has both a horizontal and vertical pixel per inch rating for working with the picture file.
A "photo quality" ink jet printer (HP C7180) we took samples from did not show any grid pattern for the ink spots but the spot spacing for each primary color tended to be around 1/200'th inch for lighter shades and with closer spacing for darker shades.
We expected that minor inaccuracies in the way dots spray from the nozzles concealed any regimented row arrangement of dots horizontally across the page for the printer we used.
Last updated April 18, 2009
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All parts (c) copyright 2009, Allan W. Jayne, Jr. unless otherwise noted or other origin stated.
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