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Understanding Bitmap Image Resolution

Everything you wanted to know about image resolution but were too embarrassed to ask.

The following questions are all typical of my postbag: "How can I turn an image I've found on the Web into a poster? How can I create a 1-inch square Web logo? What dpi settings should I use for PC and Mac screens? Why are my digital camera images too large to fit on the page? Why does my system fall over when I try to scan an image for my new 2880 dpi printer? Why don't my 400 dpi prints look any better than my 300 dpi prints?" Each question looks very different but they all centre on a single issue - Image Resolution.

Understanding image resolution is absolutely vital as it is closely involved in the output of your images both onscreen and in print. However, while it looks simple, it's actually deceptively complex and regularly leads even experienced users into making elementary mistakes. So let's start at the beginning and work our way through highlighting the common errors, pitfalls and misconceptions as we go.

Looking at the first question first - yes you can successfully turn an image you found on the Web into a poster, or even a billboard, but only if it's a vector image. Because the objects and shapes in a vector drawing are defined mathematically they are Resolution-Independent which means that they are very efficient in terms of file size and also that they can be scaled to any size with absolutely no loss of quality.

Vector drawings are defined mathematically, bitmaps are defined by their pixels.

Of course it's far more likely that your Web image won't be a vector drawing but rather a JPEG or a GIF which are both bitmap formats. Bitmap graphics are completely different to vector graphics as they are defined as a rectangular grid of Picture Elements or Pixels set when the image is first digitized. The bitmap format's big advantage is that each pixel's values can be arbitrarily different to the next which suits it perfectly to continuous-tone photographic work. The downside is that the bitmap's quality is Resolution-Dependent.

In fact there are two settings that affect the quality of the bitmap. The first is sometimes called an image's Brightness Resolution but more commonly is known as its Bit Depth, Colour Depth or Image Mode. Essentially it is the number of colours that each pixel can represent. A pixel in a typical 24-bit RGB image can represent one of 256 levels of red, green and blue which gives a possible tonal range of over 16 million colours (256 x 256 x 256). A pixel in an 8-bit indexed or grayscale image on the other hand represents one of just 256 possible values.

The second, and in this context more significant, setting is sometimes called an image's Spatial Resolution but more commonly its Pixel Dimensions. Essentially it's the number of pixels in the image both horizontally and vertically. With a pixel dimension of 300 x 300, for example, an image has a total of 90,000 pixels. With a doubled pixel dimension of 600 x 600 the image has four times as many pixels (360,000) to play with. And clearly the more pixels, or specific points of information there are in a picture, the more detail that can be represented.

Taken together the pixel dimensions and image mode provide the horizontal, vertical and depth settings that define the level of detail and tonal range in an image and hence its quality (aesthetics aside). That's why, when you use the File>New command in Photoshop, the best way to go about creating a new image it is to set the Mode to your choice of RGB, Grayscale, CMYK or Lab and then to specify the Width and Height in pixels.

The two major bitmap settings are an image's pixel dimensions and its colour mode.

So far so good - but it's noticeable that one thing we haven't mentioned so far is the image's physical size. And we've also ignored the other setting in Photoshop's New dialog, namely the Resolution. This is traditionally set in Dots Per Inch (dpi) though Pixels Per Inch (ppi) or Samples Per Inch (spi) would be more accurate (as a dot can only be on or off whereas a pixel or sample can represent any number of different values). Clearly the resolution setting maps an image's pixel dimensions to its physical size. With a pixel dimension of 600 x 600 and a resolution of 300 dpi it looks safe to say that the image has a physical size of 2 inches by 2 inches.

Unfortunately it's not quite as simple as this. By default Photoshop sets image resolution at 72 dpi and most users will have come across this being referred to as the Web standard. To create a 1 inch square Web logo then it looks self-evident that we should create an image with pixel dimensions of 72 x 72. If you do though, and then view your image at 100% or load the GIF or JPEG into your browser you're in for a surprise - your image is almost certainly smaller, might be larger, but almost certainly isn't an inch square.

When most users discover this they remember reading something about PC monitors having a screen resolution of 96 dpi compared to the Mac's 72 dpi - but in fact that's untrue in both cases and creating a 96 x 96 image will produce just as wide a range of physical onscreen sizes. If you think about it, it's inevitable. After all, you could be viewing the Web page at a screen resolution of 1600 x 1200 on a 15-inch screen or at 640 x 480 on a 21-inch screen. This means that typical CRT display resolutions can vary between approximately 40 and 120 dpi (remembering that screen sizes are measured diagonally). And, since there is a one-to-one mapping between the image and screen pixel, this means that onscreen image size can vary by a factor of 3 too.

More to the point, of course, the CRT display resolution isn't even fixed on a single monitor as you can change the resolution at any time. In other words, there is no such thing as a fixed screen size for an image. If you create one 72 x 72 pixel image at 72 dpi and another at 144 dpi they will both appear exactly the same size when viewed at 100% onscreen but this shared size will change depending on the current display resolution. The inherent factor that determines an image's onscreen size and level of detail is its pixel dimensions, the resolution setting is irrelevant. That's why when you insert an image into a Web page the <IMG> tag's width and height attributes are measured in pixels not in inches or cm.

Different resolution settings have no effect on onscreen size...

So if it makes no difference to a Web image's size if it was created at 72 dpi or 144 dpi or 1440 dpi, what function does the resolution setting play? The answer of course is print. Here there can be no flexibility. When you output a 6" x 4" print it can't vary at all, let alone by a factor of three. By fixing how many image pixels are output per inch of paper, the image resolution setting fixes the image's printed size. If you use Photoshop's Image Size command (making sure that the resampling option is not checked and that the width and height are shown in inches or cm) and then double an image's resolution, say from 72 to 144 dpi, you will see this in action as each of the width and height settings halve.

. but they do change the size of print.

When you click OK, however it looks like nothing has happened as the image is there exactly as it was before. And that's because nothing has happened. Resizing an image for print makes no difference whatsoever to the pixel data (as opposed to Resampling). In other words the resolution setting has no intrinsic effect on image quality it is really just a convenience for managing output size - handy, for example, for ensuring size-for-size print if the output resolution stays the same as the input resolution initially set in your scanner.

The resolution setting is also important when you want to change the size of your print. A typical digital camera picture of 1600 x 1200 at Photoshop's default resolution setting of 72dpi, for example, would output at over 22" x 16" - much larger than the average page. By tripling the resolution setting however, you can cut the dimensions by three and bring your image back onto the printable page. Rather more easily, you can just set the horizontal or vertical size you want in the Image Size dialog (again making sure resampling is not selected) and Photoshop will work out the necessary resolution. Alternatively you can just size or scale the image in Photoshop's Print with Preview dialog, or in your DTP application, and the application will simply work out the appropriate resolution setting to send down to your output device along with all the image's pixel data.

It's much easier to change an image's resolution implicitly by specifying its print size.

The resolution setting affects the size of the image then rather than its quality which is determined purely by the pixel information. But clearly there has to be some connection between the number of pixels and the print quality. If you output a 400 x 400 image at 40 inches square that means there are just 100 pixel's worth of data spread out over each square inch. Each pixel will be clearly and disconcertingly visible - the dreaded Pixelation that needs to be avoided at all costs. Presumably then it's desirable to have as high a resolution as possible to ensure maximum detail?

In fact that's not the case. To begin with, there's no point having greater image resolution than your output device can manage. If you're printing to a 300 dpi laser printer there's no reason to scan at over 300 dpi unless you want to be able to resize the image up. For professional use though we're more likely to be talking about output to a 1200 dpi laser or a 2400 dpi imagesetter or, these days, even a 2880 dpi inkjet (though it's worth pointing out here that equivalent dpi settings for inkjets and lasers with their scatter-gun approach just don't equate in terms of quality to an imagesetter's grid-based rigour). If you try scanning a 6" x 4" print at 2880 dpi, however, you'll see that with nearly 570 MB of data that's not a practical proposition!

Fortunately you never have to scan at these sort of resolution settings (unless you're scanning a 35mm transparency intended for much larger output). The first reason is that the eye just isn't able to resolve detail at these levels. Therefore the absolute maximum, practical, size-for-size resolution is 1000 dpi. And, crucially, this setting only relates to monochrome, solid black or white Line Art, such as scanned drawings or engravings, where one bilinear image pixel can be represented by one Device Dot that is either on or off.

For grayscale and colour images, however, the rules are totally different and this is what causes the most common misconceptions and errors. The colour printer, whether local or offset, works on a completely different model to the colour screen. The computer display can produce those 256 gray levels and 16 million colours by varying the intensity of the red, green and blue phosphors. The colour printer can't vary the level of the inks at its disposal so instead it has to mimic the effect by placing patterns of solid coloured ink dots to fool the eye.

Halftoning enables printers to simulate all shades of colour with a few solid inks.

I covered the Halftone process that produces this illusion of continuous tone grays and colours in some detail in issue 79. The fundamental point though is that the image's pixel data isn't mapped directly to device dots but rather to a grid of intermediate Halftone Spots (this is handled slightly differently for imagesetters and inkjets but the point still holds). The ultimate dpi resolution of the output device is important because it controls how many on/off device dots can be crammed into any given size of halftone spot - the more dots, the greater the number of possible combinations of dots and therefore the greater the range of possible perceived colours. In effect the Device Resolution acts as the print-based equivalent of an image's colour depth, controlling its tonal range.

And the print-based equivalent of the image's pixel dimensions is the number or frequency of the halftone spots which controls the amount of detail. This setting is variously called the Screen Frequency, Screen Ruling, Line Frequency, Halftone Frequency (you get the idea) and is measured in Spots Per Inch (spi) or, more commonly, Lines Per Inch (lpi) from the days when the halftone was actually produced with a process camera and a grid mesh. And, not surprisingly, the higher the screen frequency the more detail can be resolved and so the higher the quality of the printed image.

What is surprising though, and follows on from this, is that the image's resolution setting can be as irrelevant for print as it was for the screen. So long as there are enough pixels to match the halftone spots (this is crucial) any increase in resolution is largely immaterial - the extra image detail is simply discarded in the printed output. In other words if you output a 300, 400 or even 4000 dpi version of the same photograph to the same screen frequency, say 100 lpi, the results will be indistinguishable. You can't get more printed detail than the halftone mesh allows.

Ultimately then the final quality of the printed image is a trade-off between the level of detail and the tonal depth which depends on the number of halftone spots per inch and the number of device dots within each spot. When outputting a grayscale photograph to a 600 dpi laser printer, for example, you could choose a screen frequency of 85 lpi which means that each halftone spot is a grid of 7 x 7 dots giving a total number of grayscale levels of just 50 (49 + 1). By outputting the same image to a 2400 dpi imagesetter you could increase the line frequency to 150 lpi while still producing a halftone spot of 16 x 16, capable of discriminating a full 256 grayscale levels (or hundreds of thousands of colours if using multiple inks).

In fact it's very rare to go beyond these settings even in the most lavish high- quality coffee table book. So with a halftone frequency of just 150 lpi does that mean that there's no point scanning photographs at anything above 150 dpi size-for-size? Theoretically yes. However that would mean a mapping of just one image pixel per halftone spot. To play it safe there's a general and approximate rule of thumb that doubles the screen frequency so that each halftone spot is the averaged result of four image pixels.

What this all boils down to is that for the highest quality size-for-size monochrome line art there is never any reason to scan above 1000 dpi while for colour and grayscale output there is never any reason to scan above 300 dpi. In fact for the lower device resolution and screen frequencies of local print you can probably get away with 800 dpi and 200 dpi respectively. It's a very long way from an image scanned in at 2880 dpi but the processing time will be far faster and the output quality will be indistinguishable!

That's the good news. The bad news is that if you don't have enough pixel information to provide the desired 200 to 300 dpi output there is going to be a loss of print quality. In particular if there aren't more image pixels than there are halftone spots the results are going to become soft. Worse, if each pixel is being mapped to multiple halftone spots there will be clear pixelation.

Returning to that first question, this finally explains why you can't successfully turn a Web bitmap into a poster. If you take an image with pixel dimensions of 600 x 400 and, being generous, divide by 200, you can see that you only have enough pixel information to produce a sharp print of about 3" x 2". Next month I'll finish this tour of image resolution by taking a look at how you can stretch these limits to make the most of what pixels you do have. There's a lot that can be done, but the best option is to make sure that you have the right number of pixels for your eventual target output from the outset.

Tom Arah

April 2002

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