How Big Are My Pixels Anyway?

11 01 2010

How Big Are My Pixels Anyway?
A Guide to Understanding Resolution
© David W. Kelley and West of the Moon Photography™, all rights reserved

Judging by the number of questions I receive, resolution is probably the most misunderstood and confusing concept in all of digital photography or the digital darkroom.  If you are struggling with what resolution is all about, you are certainly not alone.  In this article I will attempt to clarify some concepts and terms.  I will also discuss the basics of how to determine the proper scanner, digital camera, and output resolution for some common output devices, and discuss the difference between image and printer resolution.  Finally, I will show how image resolution and file size are related.

In digital photography or in scanning images from film to the computer, the resolution of an image is defined by a specific number of “pixels per inch” or “ppi.”  The term “dots per inch” or “dpi” is often used interchangeably, but strictly speaking this is incorrect as dpi is more applicable to output devices such as ink-jet printers that lay down a certain number of dots of ink per inch of the image being printed.  A “pixel” (short for “Picture Element”) is a square with a specific color value and a certain physical dimension, and like a mosaic of tiles they combine to create a picture.  If the individual squares are small enough (or if the image is viewed from a distance), we perceive the image as having a continuous tone instead of many small squares of color.  Thus the image appears to have smooth, continuous transitions of color and smooth edges.

Photograph with an image resolution of 240 ppi.
Inset enlargement shows that the picture is actually
composed of square pixels arranged like mosaic tiles.
When the pixels are small enough we perceive the image
as having continuous tones of color and smooth edges.

Just as with square mosaic tiles, every pixel that makes up your image is a square of a specific color and with a specific size.  You actually determine the size of your pixels when you set the resolution of your image (in the case of digital cameras they are set for you).  If your image resolution is 72 pixels per inch then each and every pixel in your image is a square 1/72nd of in inch on each side.  If your image resolution is 300 ppi then each and every pixel in your image is 1/300th of an inch on each side and so on.  All digital cameras are set by default to capture an image at 72 ppi.  You could create an image with a resolution of one ppi, and thus each pixel would be exactly one inch square.  So as you can see, the physical size of the pixels in your image is the exact inverse of (and is therefore determined by) the resolution of the image.
Each of the square pixels that make up your image will have a specific color value.  In a pure black and white graphic image such as “line art” each pixel will be either black or white.  In computer language black or white is represented by a single digit binary number, either 0 or 1.  This is known as a single “bit” of information.  Thus pure black and white (no gray shades) images are one-bit images.   In a typical “gray scale” image, such as a black and white photograph, there are 256 possible values ranging from solid black thru varying shades of gray to pure white.  Each of these shades is represented by a binary number of eight digits or eight “bits.”  (28 equals 256 possible values).  Every eight bits makes up one “byte.”  So in a grayscale image, the tonality of each pixel takes one byte of information to record.  It is now a fairly simple matter to approximate the amount of storage space your image will occupy.  Simply multiply the pixel dimensions (length x width) to arrive at the total number of pixels.  For example if your image is 1200 x 1600 pixels then the total number of pixels in the image is 1,920,000 or 1.92 mega-pixels (mega=million).  In your gray scale image, each pixel’s color value is represented by one byte of data so 1.9 mega-pixels x one byte/pixel = 1.9 MB of data storage space is required for this image.  (For you purists out there, this is actually an approximation.  Due to vagaries within computerdom it turns out that there are actually more than a million bytes in a mega-byte.  And we wonder why we are confused!).
Now let’s look at color images.  For most purposes, the color of a pixel in a color image is a mixture of red, green, and blue in specific proportions (known as an RGB image).  If we allow for 256 possible shades of each color to be mixed we need one byte each for red, green, and blue.  It therefore takes 3 bytes of data to record the color value for each pixel (or 24 bits…3 bytes x 8 bits/byte = 24 bits and hence this is know as 24 bit color or a bit depth or color depth of 24).  To approximate the file size of an RGB image you must multiply the pixel dimensions by 3 since it takes 3 bytes to record the RGB color of each pixel.  So your 1200 x 1600 pixel RGB image will be approximately 5.7 MB in size assuming no compression (1200 x 1600 x 3 = 5.7MB).  It is also possible to determine the total number of colors that can be represented simply by multiplying the 256 shades for each of R, G, and B (256 x 256 x 256 = 16.7 million possible colors).  To produce a photorealistic print 16.7 million colors is quite adequate.  There are scanners that will record more colors (such as 36 bit and 48 bit color), but for photo quality output on most devices you are unlikely to be able to perceive the difference.  Most software and most printers will not work with these higher bit depth images (although that is changing!), and the amount of storage space required to handle these files becomes enormous.  For photo-realistic printing 24 bit color is usually just fine.
Now let’s switch gears and talk about printer resolution.  Printer resolution is given as the number of dots of ink per inch (or dpi) that the printer is capable of placing on your paper.  To the surprise of many, this number has nothing to do with the size of or the number of pixels in your image.  This is where much confusion sets in.  As it turns out, the stated resolution of ink-jet printers is somewhat misleading.  Most photo-quality ink-jet printers utilize six (or more) different colors of ink that are sprayed by nozzles to produce various sized droplets with variable spacing.  When sprayed onto paper the drops overlap, combine, or are spaced to reproduce the color of each pixel.  The printer may have to spray a drop of all six colors on top of each other  to generate a dark color.  In other words, it takes multiple drops of ink from the printer to create the color in each square pixel.  So even if the printer resolution is given as 1440 dpi it does not mean that there are 1440 dots lined up in a row in each inch of the print.  If you take six colors into 1440 it is more like 240 linear dots per inch of print that will be laid down on paper.  This will vary with the color of each pixel with darker areas requiring more ink and lighter colors less.
You can see, therefore, that you would not want to send your printer a file with the same resolution as the stated printer resolution.  In fact, sending a file closer to 240 – 360 pixels per inch is ideal as this allows the printer maximum flexibility in combining ink colors to generate the color of each pixel.  If you were to send an image sized at 1440 ppi to your printer it would simply throw out most of your data.  The worst part is that you have no idea which pixels the printer will decide to get rid of, and your results would be unpredictable.  Also, you can see that if you had to send your printer a 1440 ppi file then the 1200 x 1600 ppi image we were working with earlier would only allow you to print an image a little over an inch long!  (1600 pixels divided by 1440 pixels per inch yields an image of 1.1 inches). Sending the printer an image at 200 pixels per inch would allow you to output this same image at 6 x 8 inches at photo quality.
On the other end of the spectrum, you must send the printer pixels small enough that they can’t be seen when the photograph is viewed with the unaided eye.  Remember, the size of each pixel is inversely proportional to the resolution.  This means that as you decrease resolution; say from 240 ppi to 180 ppi, each individual pixel becomes larger in size.  It turns out that if you drop much below 180-200 pixels per inch you will begin to see deterioration in image quality as each individual pixel starts to become visible instead of giving the illusion of a continuous tone print.  This is known as pixilation.  The ideal resolution for ink-jet output is therefore between 240 and 360 ppi.  In reality, for most images, you would be hard pressed to see the difference between prints produced from a 240 ppi file and those printed from a 360 ppi file.  Outputting your images at 240 ppi will also allow you to produce larger prints.
When you are outputting your digital file to a device other than an ink-jet printer, say you are having an actual photographic print made by your local lab, you should check how they want the file sized.  The Fuji Frontier photo printer, for example works with a file sized to your desired dimensions at 300 ppi.  You will need to size your file appropriately and save it in the proper file format (usually TIFF) before sending it off to your lab for printing.
Images that will be viewed on a computer monitor such as those destined for e-mail or display on the worldwide web should be sized with a resolution of 72 – 96 ppi.  This is because image pixels will be translated directly into monitor pixels.  The size at which the image will actually be displayed is dependent on the size of the viewer’s monitor, the monitor’s resolution setting, and the actual pixel resolution of the monitor.  When the image resolution is higher than the monitor resolution, the image will be displayed on screen at a larger size than the print size.  For example, a 1 x 1 inch image with a resolution of 144 ppi would display as 2 x 2 inches on a 72 ppi monitor because the monitor needs 2 inches to display the 144 pixels in each inch of the image.  The resolution of most monitors is between 72 and 96 ppi.  So for example, if you want to e-mail an image and be sure it doesn’t exceed the size of the recipient’s monitor you might size it at 4×6 inches and set the resolution to 72 ppi.  If the recipient’s monitor is a 72 ppi monitor the image will display at 4 x 6 inches, and if they have a 96 ppi monitor the image will display at 3 x 4.5 inches.  Both would easily fit on even a small monitor without having to scroll to see the whole image.
To determine the largest size at which you can print any given image and maintain photographic quality you simply need to divide the pixel dimensions of your image by 240.  Let’s say for example that you have captured an image with your new 6 mega-pixel digital camera.  This camera captures an image that is 3000 pixels long by 2000 pixels wide (3000 x 2000 = 6 mega-pixels) and stores this image at 72 pixels per inch (the default resolution for all digital cameras).  The file as captured would produce a print of 41.6 x 27.7 inches (3000 pixels/72 pixels per inch = 41.6 inches and so on).  But we have seen that if you send your printer a 72 ppi file (assuming you could even print this big) the pixels will be visible and image quality will suffer (unless you are viewing this print from very far away).  You need to resize this image in your photo editing software to 240 ppi.  This will allow for photo quality output.  To determine the output size of this new file divide 240 into 3000 for length and into 2000 for the width.  This gives an output size of 12.5 x 8.3 inches.
If you are working with Photoshop, you can see what the maximum print size of your image will be by choosing Image>Image Size from the menu bar.  In the Image Size dialog box, un-check “resample image,” and type 240 into the resolution box.  Set the width and height dimensions to inches in their drop down boxes, and you will see the new output size of your image at 240 ppi.

Photoshop Image Size dialog box

Image Size dialog box from Adobe Photoshop.  To determine the
maximum printable output size of your image file at a resolution of
240 ppi, un-check the Resample Image box, enter 240 ppi in
the Resolution box, set the Width and Height dimensions to
inches from their drop down boxes.  The new width and
height of the image at 240 ppi will then automatically be displayed.

This same dialog box will allow you to re-size your image and change the resolution at the same time.  If you are re-sizing and/or changing the resolution of your image you should check the “resample” box and choose “bicubic” from the drop down box, then enter your desired print size and resolution in the appropriate boxes.  Be sure the “constrain proportions” check box is checked then click “OK.”  Remember, anytime you are increasing the size of your image yet keeping the resolution the same, your software will be adding pixels where there were none before.  This is known as interpolation. Photoshop does a good job as long as you are not trying to go too large.  Sharpness and image quality will suffer the more you try to enlarge an image beyond the size at which it was captured.  Always save any sharpening until after you have resized the image as the interpolation process can add artifact along already sharpened edges.

Photoshop Image Size dialog box

Image Size dialog box from Adobe Photoshop.  To resize your image
to your desired print size make sure Constrain Proportions and
Resample Image are both checked.  From the dropdown box next
to Resample Image choose Bicubic.  Enter 240 in the Resolution box
and then enter either your desired width or height — the other
dimension will fill in automatically with Constrain Proportions checked.

Let’s recap.  All digital images are made up of squares like tiles in a mosaic.  These squares are called pixels, and each pixel in your image has a specific size and a specific color value.  The size of your pixels is determined by the resolution of your image and is actually inversely proportional to resolution.  In a 24 bit color (RGB) image, there are 256 possible shades of red, green, and blue mixed to represent the color of each pixel.   256 shades of red, green, and blue can combine to produce a total of 16.7 million different colors and this is sufficient for photo-realistic output.   It requires 3 bytes of information to record and store the color of each pixel, and therefore the file size of an RGB image will be approximately three times the pixel size.
The resolution of your ink-jet printer has nothing to do with image resolution.  When printing images on an ink-jet printer your images should be sized for your desired print size (length and width), and the resolution should be set at 240-360 pixels per inch.  Images with resolutions much below 200 ppi will be of inferior quality as the pixels start to become visible.   At resolutions much above 360 ppi the printer will start to discard data.  There is no advantage in sending an image with a resolution greater than 360 ppi to your ink-jet printer.  If you are printing to another device, check with your lab (or the manual for the specific device) to determine the appropriate output resolution.  You are unlikely to be able to perceive the difference between an ink-jet print made at 240 ppi versus 360 ppi.  Images destined for e-mail or the web should have a resolution of 72 ppi as this matches the resolution of most monitors (actually 72-96 ppi) on which the images are likely to be viewed.
I hope this helps clear up some of the resolution confusion.  If you need further help or would like to comment on this article please e-mail me at David@WestoftheMoon.com, and I will reply as soon as is practical.

David W. Kelley

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