Stair Interpolation  
     
  Using a series of small increases in image size (usually referred to as stair interpolation) is a common practice to scale up an image for printing. The theory is that increasing the size of an image in small steps rather going from the original image to print size in one go yields superior results. In my experience the difference between using stair interpolation and one step interpolation varies with the image, sometimes the difference is significant, sometimes it is not. Since the process of scaling up an image  can be easily automated in Photoshop by running an action, I use stair interpolation routinely for generating images for large prints.

I was making a series of large prints recently and got so fed up having to make repeated calculations to work out how many interpolation steps were needed to get to the image size I wanted that I wrote an Excel calculator to do the work.

 

 
  The calculator works with two Photoshop actions which increase the image size in 10% or 20% steps. The Excel spreadsheet and the Photoshop actions can be downloaded from the links at the bottom of this page.

To scale up an image, enter the image size (in pixels) in the two boxes at the top of the sheet and then enter the printing resolution (in dots per inch) in the third box. The spreadsheet will now show the print sizes that will be obtained using different numbers of 10% or 20% interpolation steps. The print size table is colour coded to show similar print sizes.

Use the tables to work out whether to use the 10% or the 20% action, and make a note of how many steps are needed to generate the print size you want.

 

 
  Now run the action, switch to the history palette and click on the image size step you noted from the calculator to select the image at the required size.

If you want a precise print size, pick the step that will give the image size closest to, but smaller than, your final print size. After you have run the chosen action, make the a final image size adjustment to get to desired print size.

 

 
  Image Quality After Interpolation  
     
  The image below is a 100% view cropped from a Canon 10D image. The results of interpolating the image using 10 steps of 10% and a single step scaling to the same image size are shown below the starting image. Note the slight but visible differences in detail and colour around the puffin's eye.

 

 
 

 
   

Image scaled 10x10%

 

 
 

 
 

 

Image scaled in single step

 

 
 

 
     
  Download Photoshop stair interpolation action  
  Download Excel stair interpolation calculator