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| {{redirect|dpi}}
| | This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users. |
| {{refimprove|date=March 2011}}
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| [[Image:PrinterDots.jpg|right|frame|A close-up of the dots produced by an [[inkjet printer]] at draft quality. Actual size is approximately 0.25 inch by 0.25 inch (0.403 cm<sup>2</sup>). Individual colored droplets of ink are visible; this sample is about 150 DPI.]]
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| '''Dots per inch''' ('''DPI''', or '''dpi''')<ref name=dpi/> is a measure of spatial [[printing]] or [[video]] dot density, in particular the number of individual dots that can be placed in a line within the span of 1 inch (2.54 cm). The metric alternative is [[dots per centimetre|dots per centimeter]] (dpcm).{{citation needed|date=March 2014}} | | If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]] |
| | * Only registered users will be able to execute this rendering mode. |
| | * Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere. |
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| == DPI measurement in monitor resolution ==
| | Registered users will be able to choose between the following three rendering modes: |
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| Monitors do not have dots, but do have pixels; the closely related concept for monitors and images is [[pixels per inch]] or PPI.
| | '''MathML''' |
| | :<math forcemathmode="mathml">E=mc^2</math> |
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| Old CRT type video displays were almost universally rated in [[dot pitch]], which refers to the spacing between the sub-pixel red, green and blue dots which made up the pixels themselves. Monitor manufacturers used the term "dot trio pitch", the measurement of the distance between the centers of adjacent groups of three dots/rectangles/squares on the [[Cathode ray tube|CRT]] screen. Monitors commonly used dot pitches of 0.39, 0.33, 0.32, 0.29, 0.27, 0.25, or {{convert|0.22|mm|in|abbr=~}}.
| | <!--'''PNG''' (currently default in production) |
| | :<math forcemathmode="png">E=mc^2</math> |
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| LCD monitors have a trio of sub pixels, which are more easily measured.
| | '''source''' |
| | :<math forcemathmode="source">E=mc^2</math> --> |
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| == DPI measurement in printing == | | <span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples]. |
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| DPI is used to describe the resolution number of dots per inch in a digital print and the printing resolution of a hard copy print dot gain, which is the increase in the size of the halftone dots during printing. This is caused by the spreading of ink on the surface of the media.
| | ==Demos== |
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| Up to a point, [[computer printer|printers]] with higher DPI produce clearer and more detailed output. A printer does not necessarily have a single DPI measurement; it is dependent on print mode, which is usually influenced by driver settings. The range of DPI supported by a printer is most dependent on the print head technology it uses. A [[dot matrix printer]], for example, applies ink via tiny rods striking an ink ribbon, and has a relatively low resolution, typically in the range of {{convert|60|to|90|dpi|abbr=on}}. An [[inkjet printer]] sprays ink through tiny nozzles, and is typically capable of 300–720 DPI.<ref>[http://www.askoki.co.uk/encyclo/printertech/inkjet.asp Ask OKI—"Inkjet Printers"]</ref> A [[laser printer]] applies [[toner]] through a controlled electrostatic charge, and may be in the range of 600 to 2,400 DPI.
| | Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]: |
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| The DP measurement of a printer often needs to be considerably higher than the [[pixels per inch]] (PPI) measurement of a video display in order to produce similar-quality output. This is due to the limited range of colors for each dot typically available on a printer. At each dot position, the simplest type of color printer can either print no dot, or print a dot consisting of a fixed volume of ink in each of four color channels (typically [[CMYK]] with [[cyan]], [[magenta]], [[yellow]] and [[black]] ink) or 2<sup>4</sup> = 16 colors on laser, wax and most inkjet printers, of which only 14 or 15 (or as few as 8 or 9) may be actually discernible depending on the strength of the black component, the strategy used for overlaying and combining it with the other colors, and if it is even used in "color" mode at all.
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| Higher-end inkjet printers can offer 5, 6 or 7 ink colors giving 32, 64 or 128 possible tones per dot location (and again, it can be that not all combinations will produce a unique result). Contrast this to a standard [[sRGB]] monitor where each pixel produces 256 intensities of light in each of three channels ([[RGB]]).
| | * accessibility: |
| | ** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)] |
| | ** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)] |
| | ** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]]. |
| | ** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]]. |
| | ** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode. |
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| While some color printers can produce variable drop volumes at each dot position, and may use additional ink-color channels, the number of colors is still typically less than on a monitor. Most printers must therefore produce additional colors through a [[halftone]] or [[dithering]] process, and rely on their base resolution being high enough to "fool" the human observer's eye into perceiving a patch of a single smooth color.
| | ==Test pages == |
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| The exception to this rule are [[dye-sublimation printer]]s that utilize a printing method capable of applying a much more variable amount of dye – close to or exceeding the 256 levels per channel available on a typical monitor – to each individual "pixel" on the page without the need for dithering, albeit at an overall lower spatial resolution (typically 200 to 300dpi) that can make text and linear look somewhat rough, lower output speed (a single page requiring three or four complete passes, one for each dye color, each of which may take upwards of fifteen seconds – generally quicker, however, than most inkjets' "photo" modes), a wasteful (and, for confidential documents, insecure) dye-film roll cartridge system, and occasional color registration errors (mainly along the long axis of the page) that necessitate recalibrating the printer to account for slippage and drift in the paper feed system. These disadvantages mean that, despite their marked superiority in the field of producing good quality photographic and non-linear diagrammatic output, dye-sublimation printers remain unusual niche products, and devices using higher resolution, lower color depth and dither patterns remain the norm.
| | To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages: |
| | *[[Displaystyle]] |
| | *[[MathAxisAlignment]] |
| | *[[Styling]] |
| | *[[Linebreaking]] |
| | *[[Unique Ids]] |
| | *[[Help:Formula]] |
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| This dithered printing process could require a region of four to six dots (measured across each side) in order to faithfully reproduce the color contained in a single pixel. An image that is 100 pixels wide may need to be 400 to 600 dots in width in the printed output; if a 100×100-pixel image is to be printed inside a one-inch square, the printer must be capable of 400 to 600 dots per inch in order to accurately reproduce the image. Fittingly, 600dpi (or sometimes 720) is now the typical output resolution of entry level laser printers and some utility inkjets, with 1200/1440 or 2400/2880 being a common "high" resolution option. This contrasts with the 300/360 (or even 240) dpi of early models, and the approximate 200dpi of dot-matrix printers and fax machines, that gave faxed or computer-printed documents – especially those which made heavy use of graphics or colored block text – a characteristic "digitized" appearance thanks to their coarse and over-obvious dither patterns, inaccurate colors, loss of clarity in photographs, and jagged ("aliased") edges to some text and lineart elements.
| | *[[Inputtypes|Inputtypes (private Wikis only)]] |
| | | *[[Url2Image|Url2Image (private Wikis only)]] |
| [[Image:DPI and PPI.png|right|frame|A 10 × 10-pixel image on a computer display usually requires many more than 10 × 10 printer dots to accurately reproduce, due to limitations of available ink colors in the printer; here, a 60x60 grid is used, providing 36x the original density, compensating for the printer's lower color depth. The whole blue pixels making up the sphere are reproduced by the printer using different overlaid combinations of cyan, magenta, and black ink, and the light aqua by cyan and yellow with some "white" (ink-free) print pixels within the actual image pixel. When viewed at a more normal distance, the primary colored stippled dots appear to merge into a smoother, more richly colored image.]] | | ==Bug reporting== |
| | | If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de . |
| === DPI or PPI in digital image files ===
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| {{unreferenced section|date=January 2010}}
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| In printing, DPI (dots per inch) refers to the output resolution of a printer or imagesetter, and PPI (pixels per inch) refers to the input resolution of a photograph or image.
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| ''DPI'' refers to the physical dot density of an image when it is reproduced as a real physical entity, for example printed onto paper. A digitally stored image has no inherent physical dimensions, measured in inches or centimeters. Some digital file formats record a DPI value, or more commonly a PPI ([[pixels per inch]]) value, which is to be used when printing the image. This number lets the printer or software know the intended size of the image, or in the case of [[scanned images]], the size of the original scanned object. For example, a [[bitmap]] image may measure 1,000 × 1,000 pixels, a resolution of 1 [[megapixels|megapixel]]. If it is labeled as 250 PPI, that is an instruction to the printer to print it at a size of 4 × 4 inches. Changing the PPI to 100 in an image editing program would tell the printer to print it at a size of 10×10 inches. However, changing the PPI value would not change the size of the image in pixels which would still be 1,000 × 1,000. An image may also be resampled to change the number of pixels and therefore the size or resolution of the image, but this is quite different from simply setting a new PPI for the file.
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| For [[vector images]], there is no equivalent of resampling an image when it is resized, and there is no PPI in the file because it is resolution independent (prints equally well at all sizes). However there is still a target printing size. Some image formats, such as Photoshop format, can contain both bitmap and vector data in the same file. Adjusting the PPI in a Photoshop file will change the intended printing size of the bitmap portion of the data and also change the intended printing size of the vector data to match. This way the vector and bitmap data maintain a consistent size relationship when the target printing size is changed. Text stored as outline fonts in bitmap image formats is handled in the same way. Other formats, such as PDF, are primarily vector formats which can contain images, potentially at a mixture of resolutions. In these formats the target PPI of the bitmaps is adjusted to match when the target print size of the file is changed. This is the converse of how it works in a primarily bitmap format like Photoshop, but has exactly the same result of maintaining the relationship between the vector and bitmap portions of the data.
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| ==Computer monitor DPI standards==
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| {{mergeto|Pixel density|section=yes|date=October 2014}}
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| {{tone|section|date=October 2014}}
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| Since the 1980s, the [[Microsoft Windows]] operating system has set the default display "DPI" to 96 PPI, while [[Apple Inc|Apple]]/[[Macintosh]] computers have used a default of 72 PPI.<ref>
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| {{cite web
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| |url=http://blogs.msdn.com/fontblog/archive/2005/11/08/490490.aspx
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| |title=Where does 96 DPI come from in Windows?
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| |accessdate=2009-11-07
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| |last=Hitchcock
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| |first=Greg
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| |date=2005-10-08
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| |work=Microsoft Developer Network Blog
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| |publisher=Microsoft
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| }}</ref> These default specifications arose out of the problems rendering standard fonts in the early display systems of the 1980s, including the [[IBM]]-based [[Color Graphics Adapter|CGA]], [[Enhanced Graphics Adapter|EGA]], [[VGA]] and [[8514]] displays as well as the [[Macintosh]] displays featured in the [[Macintosh 128K|128K]] computer and its successors. The choice of 72 PPI by Macintosh for their displays arose from the convenient fact that the official 72 ''points-per-inch'' mirrored the 72 ''pixels-per-inch'' that actually appeared on their display screens. ([[Point (typography)|Points]] are a physical unit-of-measure in [[typography]] dating to the days of [[printing presses]], where 1 point by the [[Point (typography)#Current DTP point system|modern definition]] is 1/72 of the [[inch#International inch|international inch]] (25.4 mm), which therefore makes 1 point approximately 0.0139 in or 352.8 µm). Thus, a 72 pixels-per-inch seen on the display was exactly the same physical dimensions as the 72 points-per-inch later seen on a printout, with 1 pt in printed text equal to 1 px on the display screen. As it is, the Macintosh 128K featured a screen measuring 512 pixels in width by 342 pixels in height, and this corresponded to the width of standard office paper (512 px ÷ 72 px/in ≈ 7.1 in, with a 0.7 in margin down each side when assuming [[paper size#North American paper sizes|8.5 in × 11 in North American paper size]]).{{citation needed|date=April 2014}}
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| A consequence of Apple's decision was that the widely used 10 point fonts from the typewriter era had to be allotted 10 display pixels in [[em (typography)|em]] height, and 5 display pixels in ''[[x-height]]''. This is technically described as 10 ''pixels per em'' (''PPEm''). This made 10-point fonts render crudely and difficult to read on the display screen, particularly for lowercase characters. Furthermore, there was the consideration that computer screens are typically viewed (at a desk) at a distance 1/3 or 33% greater than printed materials, causing a mismatch between the perceived sizes seen on the computer screen versus those on the printouts.{{citation needed|date=April 2014}}
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| [[Microsoft]] tried to solve both problems with a hack that has had long-term consequences for the understanding of what DPI and PPI mean.<ref name="msdn-greg">{{cite web |url=http://blogs.msdn.com/fontblog/archive/2005/11/08/490490.aspx |title=Where does 96 DPI come from in Windows? |accessdate=2010-05-09 |first=Greg (fbcontrb) |date=2005-09-08 |publisher=blogs.msdn.com}}</ref> Microsoft began writing its software to treat the screen as though it provided a PPI characteristic that is <math>\tfrac{4}{3}</math> of what the screen actually displayed. Because most screens at the time provided around 72 PPI, Microsoft essentially wrote its software to assume that every screen provides 96 PPI (because <math>72 * (1+\tfrac{1}{3}) = 96</math>). The short-term gain of this trickery was twofold: | |
| *It would seem to the software that <math>\tfrac{1}{3}</math> more pixels were available for rendering an image, thereby allowing for bitmap fonts to be created with greater detail.
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| *On every screen that actually provided 72 PPI, each graphical element (such as a character of text) would be rendered at a size <math>\tfrac{1}{3}</math> larger than it "should" be, thereby allowing a person to sit a comfortable distance from the screen. However, larger graphical elements meant less screen space was available for programs to draw; indeed, although the default 720-pixel wide mode of a Hercules mono graphics adaptor (the one-time gold standard for high resolution PC graphics) – or a "tweaked" VGA adaptor – provided an apparent 7.5-inch page width at this resolution, the more common and color-capable display adaptors of the time all provided a 640-pixel wide image in their high resolution modes, enough for a bare 6.67 inches at 100% zoom (and barely any greater visible page ''height'' – a maximum of 5 inches, versus 4.75). Consequently, the default margins in Microsoft Word were set, ''and still remain'' at 1 full inch on all sides of the page, keeping the "text width" for standard size printer paper within visible limits; despite most computer monitors now being both larger and finer-pitched, and printer paper transports having become more sophisticated, the Mac-standard half-inch borders remain listed in Word 2010's page layout presets as the "narrow" option (versus the 1-inch default).{{citation needed|date=April 2014}}
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| *Without using supplemental, software-provided zoom levels, the 1:1 relationship between display and print size was (deliberately) lost; the availability of different-sized, user-adjustable monitors and display adaptors with varying output resolutions exacerbated this, as it was not possible to rely on a properly-adjusted "standard" monitor and adaptor having a known PPI. For example, a 12" Hercules monitor and adaptor with a thick bezel and a little underscan may offer 90 "physical" PPI, with the displayed image appearing nearly identical to hardcopy (assuming the H-scan density was properly adjusted to give square pixels) but a thin-bezel 14" VGA monitor adjusted to give a borderless display may be closer to 60, with the same bitmap image thus appearing 50% larger; yet, someone with an 8514 ("XGA") adaptor and the same monitor could achieve 100 DPI using its 1024-pixel wide mode and adjusting the image to be underscanned. A user who wanted to directly compare on-screen elements against those on an existing printed page by holding it up against the monitor would therefore first need to determine the correct zoom level to use, largely by trial and error, and often not be able to obtain an exact match in programs that only allowed integer percent settings, or even fixed pre-programmed zoom levels. For the examples above, they may need to use respectively 94% (precisely, 93.75) – or 95/90, 63% (62.5) – or 60/66.7; and 104% (104.167) – or 105, with the more commonly accessible 110% actually being a less precise match.{{citation needed|date=April 2014}}
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| Thus, for example, a 10-point font on a Macintosh (at 72 PPI) was represented with 10 pixels (i.e., 10 PPEm), whereas a 10-point font on a Windows platform (at 96 PPI) at the same zoom level<!--"on the same screen" text removed because of both a) Mac and Windows monitors being mutually incompatible at the time, before Mac moved to using multisync VGA monitors re-engineered to use their proprietary socket standards, b) it doesn't actually matter what the screen is, in terms of physical size, or logical or physical resolution, because at the moment we're talking purely about the virtual display surface inside the computer itself, which can be of arbitrary resolution so long as it's big enough to show at least one text character--> is represented with 13 pixels (i.e., Microsoft rounded 13.3333 to 13 pixels, or 13 PPEm) – and, on a typical consumer grade monitor, would have physically appeared around 15/72 to 16/72 of an inch high instead of 10/72. Likewise, a 12-point font was represented with 12 pixels on a Macintosh, and 16 pixels (or a physical display height of maybe 19/72 of an inch) on a Windows platform at the same zoom, and so on.<ref>
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| {{cite web
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| |url=http://www.microsoft.com/typography/tt/sbit.aspx
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| |title=Microsoft Typography – Making TrueType bitmap fonts
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| |accessdate=2009-11-07
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| |last=Connare
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| |first=Vincent
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| |date=1998-04-06
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| |publisher=Microsoft
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| }}</ref> The negative consequence of this standard is that with 96 PPI displays, there is no longer a 1-to-1 relationship between the font size in pixels and the printout size in points. This difference is accentuated on more recent displays that feature higher [[pixel densities]]. This has been less of a problem with the advent of [[vector graphics]] and fonts being used in place of bitmap graphics and fonts. Moreover, many Windows software programs have been written since the 1980s which assume that the screen provides 96 PPI. Accordingly, these programs do not display properly at common alternative resolutions such as 72 PPI or 120 PPI. The solution has been to introduce two concepts:<ref name="msdn-greg"/>
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| *'''logical PPI''': The PPI that software claims a screen provides. This can be thought of as the PPI provided by a virtual screen created by the operating system.
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| *'''physical PPI''': The PPI that a physical screen actually provides.
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| Software programs render images to the virtual screen and then the operating system renders the virtual screen onto the physical screen. With a logical PPI of 96 PPI, older programs can still run properly regardless of the actual physical PPI of the display screen, although they may exhibit some visual distortion thanks to the effective 133.3% pixel zoom level (requiring either that every third pixel be doubled in width/height, or heavy-handed smoothing be employed).{{citation needed|date=April 2014}}
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| == Proposed metrication ==
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| {{see also|dots per centimeter}}
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| There are some ongoing efforts to abandon the DPI unit in favor of [[metrication]], giving the inter-dot spacing in [[dots per centimeter]] (dpcm) or [[micrometer]]s (µm) between dots.<ref>{{cite web|url=http://java.sun.com/j2se/1.4.2/docs/api/javax/print/attribute/ResolutionSyntax.html|title=Class ResolutionSyntax|publisher=Sun Microsystems|accessdate=2007-10-12}}</ref><ref>{{cite web| url=http://www.w3.org/TR/css3-mediaqueries/| title=Media Queries}}</ref> A resolution of 72 DPI for example equals a resolution of about 28 dpcm or an inter-dot spacing of about 350 µm. In [[BMP file format#Example 1|BMP images]] 2835 pixels per meter correspond to 72 DPI (rounded 2834.6472).
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| {| class="wikitable"
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| |+Conversion table
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| |-
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| ! DPI <br>(dot/in) !! dpcm <br> (dot/cm) !! Pitch<br> (µm)
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| |-
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| |align=right| 72
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| |align=right| 28
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| |align=right| 350
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| |-
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| |align=right| 96
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| |align=right| 38
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| |align=right| 265
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| |-
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| |align=right| 150
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| |align=right| 59
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| |align=right| 169
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| |-
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| |align=right| 300
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| |align=right| 118
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| |align=right| 85
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| |-
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| |align=right| 2540
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| |align=right| 1000
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| |align=right| 10
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| |-
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| |align=right| 4000
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| |align=right| 1575
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| |align=right| 6
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| |}
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| == See also ==
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| * [[Pixels per inch]]
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| * [[Samples per inch]] – a related concept for [[image scanner]]s
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| * [[Lines per inch]]
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| * [[Metric typographic units]]
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| * [[Display resolution]]
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| * [[Mouse dpi|Mouse DPI]]
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| * [[Twip]]
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| == References ==
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| {{Reflist|refs=
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| <ref name="dpi">
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| The acronym appears in sources as either "DPI" or lowercase "dpi".
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| See: [http://www.office.xerox.com/latest/XOGFS-17 <!--
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| --> "Print Resolution Understanding 4-bit depth – Xerox"] (PDF).
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| Xerox.com. September 2012.
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| </ref>
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| }}
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| == External links ==
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| *[http://www.rideau-info.com/photos/mythdpi.html All About Digital Photos – The Myth of DPI]
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| * [http://www.infobyip.com/detectmonitordpi.php Monitor DPI detector]
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| {{DEFAULTSORT:Dots Per Inch}}
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| [[Category:Printing terminology]]
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| [[Category:Units of density]]
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| [[Category:Computer printing]]
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