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Numbers & Details

Math for Print File Sizes
Math for Image Displays
Image Display Crops and Print Sharpness

Math for Print File Sizes

The lab printing my images with a Lightjet5000, uses a TIF file resolution setting of 304.8 pixels per inch. That is 304.8/2.54 = 120 pixels per centimeter. When viewing image pages, note the full print sizes shown in inches just below image titles. There are three RGB bytes totaling 24 bits per pixel. Therefore some typical file sizes used in printing are roughly:

          12x18 prints: 3(12*304.8)(18*304.8)    =  3(3657 x  5486 pixels) =  60 megabytes
          14x21 prints: 3(14*304.8)(21*304.8)    =  3(4267 x  6401 pixels) =  82 megabytes
    19.6x24.6 prints: 3(19.6*304.8)(24.6*304.8)  =  3(5974 x  7498 pixels) = 134 megabytes
    21.6x26.6 prints: 3(21.6*304.8)(26.6*304.8)  =  3(6583 x  8108 pixels) = 160 megabytes
    23.6x29.6 prints: 3(23.6*304.8)(29.6*304.8)  =  3(7193 x  9022 pixels) = 195 megabytes
    28.6x37.6 prints: 3(28.6*304.8)(37.6*304.8*) =  3(8717 x 11460 pixels) = 300 megabytes 

Math for Image Displays

Photographers putting valuable fine art images on the World Wide Web for customers balance needs of displaying images showing enough detail to provide an adequate sense of an image's aesthetic against being small enough that they don't invite unauthorized use. Accordingly images on such web pages appear relatively small with limited detail. Any of us would prefer to be able to web display to customers the full sized beauty of images as it would obviously result in more sales. Particularly with larger prints, much of the aesthetic is in the fine details impossible to convey with a small image display. To counter that limitation I have chosen to display additional image crops discussed below.

These web display images are directly derived from the actual Photoshop 6.0 PSD master image files which have an Adobe (1998) profile. Note for printing, PSD files are Lightjet5000 printer profiled to create TIF print files. For web display, PSD files are converted to standard web profile, sRGB IEC61966-2. Resulting files are not manipulated except for slight unsharp masking after size reduction in order to provide a reasonably faithful display of hue, saturation, and luminance. However the actual prints will usually display a bit flat or unsaturated because of limitations with conversion to sRGB along with monitor gamma. In any case web browsers as discussed above do not have any mechanism for controlling color and it is quite unlikely receiving monitors are color calibrated.

Images on both my home page image index and on individual image pages are all scaled relative to actual print sizes. The gallery index thumbnails are all scale at 1/(50x50) or 1/2500. On image pages, film formats have been reduction scaled at a different ratio between print size and web display in order to better accommodate browser screen space while still conveying a sense of print size. 35mm images are HW dimension scaled at 10% or 1/10, 6x7 images at 8.5% or 1/11.7 and 4x5 images at 7.5% or 1/13.3. Because it is an area square function, the file size ratios are far smaller, ie 1/178 for 4x5. To view an entire 30x38 inch 4x5 image on a single screen given a dot pitch of typical monitors would require a screen dimension of 7.5x9.5 feet!

    12 x 18 inch 35mm:  (3658 x  5486 pixels)0.100  = 366 x 549 pixels or 1/100 print size
    20.6x26.6 inch 6x7: (6279 x  8108 pixels)0.085 = 534 x 689 pixels or 1/138 print size
    29.6x37.6 inch 4x5: (9022 x 11460 pixels)0.075  = 677 x 860 pixels or 1/178 print size

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Image Display Crops and Print Sharpness

In order to provide a token display similar to actual print resolution, each image page also contains a link to small sections of the full print file image, referred to as a crops. Per above , the crop is also directly derived from the actual Photoshop PSD file. On each page the highlighted link is located just below image titles. These 303x303 pixel crops have been reduction scaled 33% from actual 909x909 pixel image file sections they were sampled from. That takes into account the difference between approximate monitor dot pitch of 100 pixels per inch and print file pixels of 304.8 pixels per inch. Thus the crops will display at the approximate size of viewed prints or 3x3 inches if one runs at XVGA or SXGA desktop sizes with a typical monitor. Doing so removes some detail but gives a better sense of detail than displaying at 100% which would display at about three times the viewed print size. After the 1/3 reduction they were slightly unsharped masked to compensate for the re-size. Therefore actual prints appear somewhat sharper than the displayed monitor crops.

Here is an example from the 4x5 04-I1-2 image page :
view 04-I1-2 image page 33% crop
view print 100% resolution crop
view full image

Most images have two crops displayed via the link, one above the other. The lower crops are selected from foregrounds near frame bottom. Upper crops are selected from backgrounds higher on frames, which are at a far distance and below any skyline. Camera lenses have limited depth of field which means limited ability to capture objects in sharp focus at both near and far distances. Thus I am providing a crop from each distance indicating that I focused correctly and likely used a very small lens aperture. For 4x5 images that also includes proper position of view camera movements like tilt. For images in which all parts of a frame are about the same distance, there is just one crop. For example close ups of wildflowers or a distant landscape without a foreground. Crops open in separate windows. Thus one should not be using a browser's full screen display mode. Instead size each window for non overlapping panes so a crop window just needs to be a few inches wide.

Crops from 4x5 images will appear sharper than 6x7 crops which will be sharper than 35mm crops. In fact the 4x5 image crop above shows considerable fine detail even when displayed at 100%. That is despite the fact the ratio of crop size to full image becomes larger with the smaller prints.

    12x18 inch 35mm:  4.2% 0f full print size
    14x21 inch 35mm:  2.3% 0f full print size
    23.6x29.6 inch 6x7: 1.3% 0f full print size
    28.6x37.6 inch 4x5: 0.8% 0f full print size

This is primarily due to the ratios of print area to sourced unit film area shown below. And correspondingly such carries over to the actual prints. For example there is three times as much film area available for 4x5 printed to 38 inches as 35mm printed to 21 inches. Note with a high end drum scanner, the full rich detail from a transparency may be extracted regardless of its size. That is because media is located on a transparent rotating drum under micro stepper motor control between the optical path of focused light source and just three highly designed and calibrated photomultiplier sensors. Each sensor has far more dynamic range and characterization than any given cell of a CCD area array of millions of tiny sensors. Flatbed or film scanners, outside an Imacon, rely on a fixed lens focusing on fixed media between a large diffuse light source.

        12x18 inch print     to 1x1.5 inch 35mm film frame = 144:1
        14x21 inch print     to 1x1.5 inch 35mm film frame = 196:1
    19.6x24.6 inch print to 2.17x2.76 inch 6x7  film frame =  81:1 
    21.6x26.6 inch print to 2.17x2.76 inch 6x7  film frame =  96:1 
    23.6x29.6 inch print to 2.17x2.76 inch 6x7  film frame = 116:1 
    28.6x37.6 inch print        to 4x5 inch 4x5 film frame =  54:1

David Senesac
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