Generating High Quality Ink Jet Prints

Making effective use of professional photographic ink jet printers is tricky business, especially when the statistics that are commonly used to describe these printers are vague and misleading. Learning how a ink jet printers function, how to properly interpret their capabilities, and make the most effective use of those capabilities, is possible. You may need to deal with a little mathematics to fully understand, but for those brave enough to endure, your answers are below.

Terminology

In the printing world, there are numerous terms used to describe the various aspects of a printers behavior. Everyone has heard of DPI, many of you have heard of PPI, but not everyone understands the true meaning of these terms and how they relate.

• Pixel: Smallest unit of an image.
• Dot: Smallest element of a print generated by a printer.
• DPI: Dots per Inch
• PPI: Pixels per Inch

Understanding terms is important, but everything has context, and understanding how these terms relate to each other in the context of ink jet printing is critical to learning how to generate the best quality prints. Every image is composed of pixels, and every pixel in an image represents a single distinct color. The color of a pixel may be produced in a variety of ways, from the blending of RGB light on a computer screen, to a solid mixture of dye in a dye sublimation printer, to the dithered composition of colored dots printed by an ink jet printer. The latter is of interest here.

PPI to DPI Relationship

When an ink jet printer renders an image, it has a limited set of colors to work from, usually cyan, magenta, yellow, and black. Higher-end printers may include a variety of other colors as well, such as blue, orange, red, green, and various shades of gray. To produce the wide range of colors expected of a photo printer, multiple dots of each color must be combined to create a single color as represented by a pixel. A dot may be smaller than a pixel, but should never be larger. The maximum number of dots that an ink jet printer may lay down in a single inch is the measurement of DPI. Since multiple printer dots must be used to represent a single pixel, the PPI of a printer will never be as high as the printers maximum DPI.

The Human Eye

Before diving into the details of how to achieve maximum print quality, it is important to understand how the human eye sees a print. The eye is an amazing device, and as photographers, we know that better than most. It can see amazing clarity and dynamic range. It also has a limit on its ability to resolve detail, and that directly affects what resolution you may choose to print at.

Resolving Power

The maximum resolving power of the human eye is lower than printer manufacturers would have you believe, which tends to be 720ppi or 600ppi, depending on the manufacturer. It is also lower than most print fanatics would have you believe, as well. Depending on the intended viewing distance, the lowest acceptable PPI may be considerably lower than you might expect. The most general way to describe the resolving power of the human eye is as one arcminute, or 1/60th of a degree, at any distance (for the average eye...those with 20/10 vision see about 30% better, or 1/86th of a degree acuity.) For normal vision, we can use this to approximate the minimum resolvable size of a pixel at a given distance, so assuming a hand-held viewing distance of about 10 inches for a 4x6 inch print:

[tan(A) = opposite / adjacent ]

tan(arcminute) = size_of_pixel / distance_to_image
tan(arcminute) * distance_to_image = size_of_pixel
tan(1/60) * 10" = 0.0029" min pixel size

For sanity sake, we can make the tangent of arcminute, or resolving power P, a constant:

P = tan(arcminute) = tan(1/60) = 0.00029

This may be translated into pixels per inch like so:

1" / 0.0029" = 343.77 ppi

The minimum resolvable pixel size may be calculated for any distance, and as distance increases, the minimum required PPI will shrink. If we assume an 8x10 print at a viewing distance of around a foot and a half, we would have the following:

1" / (0.00029 * 18") = 191.5 ppi

A general formula for this can be created, where D is the viewing distance:

1/(P*D) = PPI

As a simple rule, regardless of how close you may view a photograph, the unaided 20/20 eye is incapable of resolving more than about 500ppi (for those with 20/10 vision, resolving power reaches about 650ppi.) The only reason one may surpass a resolution of 500ppi is when you require more than a standard 300-360ppi, and you need to stay within the limitations of your hardware (i.e. 600ppi for Canon printers.)

Resolving Power for 20/10 Vision

While the very vast majority of the time, you will not need more than 300-360ppi, if you do have very fine detail that requires a high PPI, you may wish to base your calculations on a higher visual acuity. For viewers with 20/10 vision, visual acuity is a bit improved, at around 1/86th of a degree (0.7 arcminute). The constant P at this level of acuity is smaller, and therefor necessitates a smaller pixel when printing images with very fine detail.

Given our formula from before, adjusted for improved acuity:

P = tan(arcminute) = tan(1/86) = 0.00020

Taking our 4x6" print viewed at 10", and plugging this into our general formula for PPI, we would have a PPI of:

1" / (0.0002 * 10") = 1" / 0.002" = 500 ppi

Ok, enough math for now. On to the good stuff.

Print Resolution

Now that we know the limits of the human eye, we can better determine what resolution to print at for a given paper size and viewing distance. An ink jet printer is not capable of producing ideal results at any PPI, so we must compromise, and choose a resolution that is more appropriate to the hardware. Anyone who has investigated the "best" resolution to print at has likely come across many common terms, such as 240ppi, 300ppi, 360ppi, 720ppi, etc. These numbers are often based in truth, but when to use them, and when you might actually choose a lower resolution, is often left unexplained.

When choosing a resolution to print at, you must make sure it is divisible into the lower bound of the DPI your printer is capable of. In the case of an Epson, this is likely 1440, and in the case of a Canon it is likely to be 2400. Every printer has a native internal pixel resolution that any image printed will be resampled to. In the case of Epson, this is usually 720ppi, and in the case of Canon it is usually 600ppi. The PPI of printers is rarely publicized by the respective manufacturers, so it is up to you to figure it out. A handy little tool called PrD, or Printer Data, can help. Just run, and your printers native PPI will be displayed.

Optimal Resolution

Determining the optimal resolution to print at, now that we have both the printers DPI and native PPI, should be a trivial task: use the native PPI. While this seems logical, there are many reasons why this is less than idea. For one, 720ppi is well beyond the maximum resolving power of the human eye (@500ppi). Using the maximum resolution is also likely to use more ink (wasting money), while also reducing your tonal range. More on tonal range in a bit.

If we assume a minimum viewing distance of approximately six inches for a 4x6 print, the theoretical PPI would be about 575ppi. This rounds up to a printer-native 600ppi on Canon, and 720ppi on Epson. A viewing distance of six inches for a person with 20/20 vision (corrected or otherwise) is extremely close, and rather unlikely. If we assume a more realistic minimum viewing distance of ten inches, our theoretical PPI drops to about 350.

If we printed our 4x6 photo at a resolution of 350ppi, the results would likely be less than stellar. For one, 350 is not evenly divisible into either 600 or 720, which will cause the printer driver to do some rather unsightly, distorted scaling for us. Any regular, repeating patterns will show up with very undesirable moiré, which can greatly reduce the quality of a print. Choosing a resolution that evenly divides into the native printer resolution, such as 360ppi for Epson, or 300ppi for Canon, will help ensure that any scaling the driver does will produce even results.

Here are some common print resolutions for various DPI's:

  1200 | 1440 | 2400  
 =-=-=-=-=-=-=-=-=-=-=  
       |      | 1200*  
   600 |  720 |  600  
   400 |  480 |  400  
   300 |  360 |  300  
   240 |  288 |  240  
   200 |  240 |  200  
   150 |  180 |  150  

* Highly unlikely to ever be needed or used.

Tonal Range

Despite all the knowledge we now have, knowing the native resolution of a printer is not really enough to choose an appropriate PPI. There is another issue that should be addressed first, and that is one of tonal range. The process of generating a photograph from a vision is one of continual reduction in color range and contrast. The human eye is capable of considerable dynamic range, however the camera is capable of considerably less. Printers are capable of still less, so making the most effective use of your printer's capabilities is key to producing a high quality, professional print.

The tonal range that may be reproducible by a printer is ultimately determined by the cell size of a pixel. If we take the ever present Epson printer, with its 1440 DPI, we can determine the number of dots per pixel with a simple formula:

(DPI / PPI) * 2 = DPP

If we assume the native resolution, our Epson printer can produce 4 dots per pixel:

(1440/720)*2) = 4

These four dots must produce a square pixel, so in actuality the dots per pixel are arrayed in a 2x2 cell. If we half our ppi, and use 360 instead, we get a 4x4 cell, and at 288ppi we get a 5x5 cell. This simple fact is directly responsible for the ultimate tonal range a printer is capable of, as the number of dots at 720ppi is 1:4 what it is at 360ppi, and 1:6.25 what it is at 288ppi. As we reduce our PPI, we increase the number of colors that may be represented at each individual pixel. At 180ppi, we have theoretically eight times as much tonal range as we do at 720ppi.

If we update our common print resolutions table with cell sizes, we have the following (note, 2400dpi has been normalized with 1200dpi):

      | 1200 | 1440 | 2400  
 =-=-=-=-=-=-=-=-=-=-=-=-=-=  
  2x2 |  600 |  720 |  600  
  3x3 |  400 |  480 |  400  
  4x4 |  300 |  360 |  300  
  5x5 |  240 |  288 |  240  
  6x6 |  200 |  240 |  200  
  8x8 |  150 |  180 |  150  

A 7x7 cell is not evenly divisible, and has been excluded. Given the chart above, it should become clearer why, despite lowering the PPI from say 720 to 360, a print can still look superb. For a close viewing distance of eight inches, we are within the limit of resolving power, and we gain tonal range. Dropping even farther to 288ppi will likely increase tonal range more, without any tangible visible detriment to the vast majority of viewers. The added tonal range at a close viewing distance, however, will likely improve the overall quality of the print for the same majority of users, as the human eye is capable of detecting many millions of colors over an extremely broad range of tones.

Theoretical vs. Actual

Quite often we run into the issue of the theoretical vs. the actual, and usually the actual is less appealing than the theoretical. In the case of Ink Jet printers, the theoretical may actually represent less than the actual capabilities of a printer. In particular, the actual achievable tonal range is often higher than is theoretically derivable via the above formula due to the differences in horizontal vs. vertical DPI. To determine the resolution of a print, you must base your calculations on the lower DPI bound. In the case of a 2880x1440 Epson, this lower bound is 1440. However, because the horizontal DPI is twice as much, you effectively get twice as many dots.

This results in the desirable effect of increasing the possible tonal range at any given resolution. Since our Epson printer has 2880 pixels in the horizontal, at 720ppi we actually have a cell that is 4x2. At 360ppi we have a cell that is 8x4, and at 288ppi we have a cell that is 10x5. Assuming 8 different ink colors, that comes out to a theoretical 401 (400 + 1 extra for pure white...or the absence of ink) possible tones at 288ppi, which is more than enough to produce a tremendously wide range of color. Canon PIXMA Pro printers technically offer even greater range, as their vertical resolution is 2400 rather than 1440, and the horizontal resolution is 4800 rather than 2880. At 240dpi you get a 20x10 size pixel cell, with 9 inks you have 1801 possible tones. A Canon at 300ppi, you have the same tonal range as an Epson at 288ppi. Despite having a lower maximum PPI of 600, Canon printers should produce better tonal range at any given pixel size.

The picture is even more complex, however, as modern professional-grade ink jet printers use not only a variety of ink colors, they also use varying ink droplet sizes. Assuming three different drop sizes (common for Epson and and Canon), theoretically that increases the range of tones to 1203. The realistic effect of varying droplet size is more even tonal grades, rather than considerably more tonal range, however the end result is basically the same: better looking images.

Tonal grading can also be addressed using additional colors - eg CcMmYK which uses Light Magenta and Light Cyan; or even a true Black. Tonal grading also has an impact on image resolution since dot spacing is used to create lighter tones where lighter inks are not available.

Beyond all of this theory there are physical and practical limitations that, once again, take away all the gains our theory has given us. The maximum tonal range that may be achievable is dependent on more than just ink picoliters and mathematics. Paper is a critical factor in determining tonal range, and papers range from soft and warm to stunning bright, from glossy to matte, from smooth to rough. Choosing a paper, however, is a discussion for another day.

Conclusions

Knowledge is power, as they say, or in the case of photography, knowledge is a better vision envisioned. Despite all the rhetoric about printers on the internet, both from manufacturers and avid consumers, a little math and some logic can provide some useful knowledge. If you take anything away from reading this far today, I hope its that resolution is not the most important factor when it comes to creating a stunning print. Viewing distance and tonal range are just as important, if not more important.

As a general rule of thumb, 240-360ppi for your average professional grade ink jet printer will be sufficient for the vast majority of prints viewed within a couple feet. Larger prints framed and hung, viewed at a distance of several feet could do with 200-240ppi. Giant prints viewed at more than a few feet, such as wrapped canvas, can easily do with the bare minimum of 150-180ppi. Using the proper resolution has the benefit of improving tonal range, and will likely reduce your overall ink usage as well.

Empirical Study: Does PPI Really Matter?

For all of the theory above, thats all it currently is...theory. It is the end result of days of research on the physical characteristics of printers, the theory behind printing and ink, the concepts of DPI and PPI, etc. The real question is, how does it stack up against empirical evidence? Does it withstand the test of reality?

In this small study, I'll be looking at whether choosing a higher PPI over a lower one really matters. The theory states that the human eye has high, but limited, resolving power. In the case of a 4x6 print intended for close hand-held viewing, does printing at 600ppi vs. the more common 240ppi offer any benefit? Hopefully a visual demonstration will help shed some light on the issue, and put theory into practice.

The Subject

For this particular study, I took a shot of a small house fly that was enjoying some Mango rinds. I thought it would make an interesting subject of study, as a fly, even shot at macro scale, is riddled with extremely fine details that are normally well beyond the resolving power of the human eye. The scene covered a fairly high range of contrast, from the relatively bright yellow/orange mango peel to the nearly black fly. The scene was lit with natural light from behind and tungsten light in the foreground to bring out detail in the eyes and thorax.

The shot was created with a Canon EOS 450D (Rebel XSi) cropped-sensor body and the Canon EF 100mm f/2.8 USM Macro lens. The shot was taken at f/8, ISO 800, and exposed for 1/6th of a second in natural light. It was imported as a RAW .cr2 file to disk, all workflow was done directly from RAW. The original image was 4272x2848, however it was cropped to 2295x1530 to enlarge the subject and fill most of the frame. At that screen resolution, it translates into a 3.83x2x55" print @ 600PPI, or a 9.56x6.38" print @ 240ppi.

The Test

The test is fairly simple. The original photo was cropped to create a sufficiently large subject, which took up approximately 1/6th of the total photo area initially. It was color corrected with a proper white balance, an exposure was slightly adjusted to lighten blacks, which were too dark to print well. A slight amount of noise reduction and sharpening was also applied.

Two prints were generated from Adobe Lightroom 3. The prints were generated by a fairly cheap Canon iP4500 5-ink CMYK printer with a native 9600x2400 dpi. The first was a 600ppi borderless print on 4x6" Canon Photo Paper Plus Glossy II paper. The second print was a 240ppi borderless print on the same type of 4x6" paper. Both prints were allowed to dry for about 12 hours, as full detail does not generally appear on prints made with ChromaLife100+ ink until it has dried and cured for a time.

Both prints were finally scanned into Adobe Photoshop a Canon CanoScan 8800F. (Now that I'm writing this, I'm shocked at how much Canon gear I have...that was never intentional...Guess its time to buy an Epson printer...) Scans of both prints were made at 600dpi, this particular scanners maximum "photo" scanning resolution. Crops of the eye and the wing joint of the fly were made at 100% resolution from both the 600ppi and 240ppi print for comparison.

The Results

All sharpening and post processing options for the scanner were disabled. No additional post processing was done in Photoshop after the scans were complete. The images below are unmodified, raw scans.

Crop #1: Fly Eye

The crop of the eye, which includes parts of the head and appendages, is an excellent example of fine details. A comparison of both resolutions may be seen below:

Eye @ 600 ppi

Eye @ 240 ppi

Image Evaluation

From these two crops, it is clear that the 600ppi print definitely renders finer details much better. The detail in the eye is mostly preserved. An appendage that contained fine details is also clearly sharper and more defined in the 600ppi print. However, the 600ppi print also picks up image noise better, which degrades some of the smoother areas of the image.

Tonal range appears to be slightly better in the 240ppi print, however not significantly. This seems to debunk the idea that printing at lower resolutions theoretically offers greater tonal range per pixel. This is likely due to the fact that the printer does not support alternative line heights and always prints at 600ppi (scaling images up as necessary internally.) Given that the 600ppi print is actually closer to a 4x3" print size, manually scaling the image up to the proper resolution for a native 600ppi print could likely extract more detail than is currently visible.

Based on these images, one would expect that printing at 600ppi would always generate a better, clearer, sharper print.

Print Evaluation

The actual physical print is a slightly different story than the scanned crops above. The eye detail is not really that visible to the naked eye at a viewing "comfortable" hand-held viewing distance. At about 3-4 inches, detail in the eye can barely be seen, and at about 2-3 inches, it can be seen but not extremely clearly. (This may change if the image is manually scaled to exactly the right screen resolution for a 600ppi print, and appropriately sharpened. Another test will need to be done to verify.) On the other hand, the very fine but higher-contrast details of the appendage, as well as many other appendages and hairs in the full photo, clearly appear sharper at 600ppi.

Crop #2: Fly Wing Joint

The crop of the wing joint is a lower contrast shot. The aim here is to determine if details spanning a larger low-contrast area benefit from printing at a higher PPI.

Wing @ 600 ppi

Wing @ 240 ppi

Image Evaluation

This crop is a little harder to discern. There is some additional detail at 600ppi, however the difference is minor compared to 240ppi. Image noise is definitely picked up here, and definitely degrades the overall tonal range of the image compared to the lower resolution crop. As a lower contrast area, the differences don't seem worth the higher printing resolution.

Print Evaluation

Surprisingly, although the differences when evaluated from scanned crops seem negligible, the finer details of the 600ppi print are recognizable by the naked eye at a comfortable viewing distance. While the wing joint at 240ppi appears to be a fairly smooth and continuous color, fine streaks of detail are visible at 600ppi. In other parts of this crop, however, finer details brought out at 600ppi are not readily visible over the 240ppi print.

Final Conclusion

Despite the theory indicating that a print resolution above approximately 360ppi will not generate detail resolvable by the naked eye, actual tests seem to prove differently. The scanned crops clearly show that there is greater detail produced by the 600ppi prints over the 240ppi prints. This detail includes a greater degree of image noise, however this is rarely visible when prints are viewed at a proper viewing distance. In lower contrast areas, fine details are difficult if not impossible to resolve at a comfortable hand-held viewing distance. However, areas of fine detail with greater contrast do appear clearer and sharper at a hand held distance. This may or may not be immediately recognized, however given a few moments of examination, and the difference is apparent. The fine hairs and appendages are definitely more soft at 240ppi, but are very sharp at 600ppi. Some very fine details visible along the fly's legs nearly disappear completely at 240ppi, but are visible at 600ppi on closer inspection. As the Canon iP4500 prints at only a single resolution...600ppi, no additional tonal range is visible in the 240ppi print outside of what is gained by less image noise.

Specific results may differ with different types of printers. Professional Ink Jet printers seem to always print at only one resolution, with only a single line height (pixel cell size). Other types of printers that offer dynamic cell size may produce different results, and may offer less detail but improved tonal range.

Emprical Study: Extreme digital upscaling

For all of the theory above, thats all it currently is...theory. It is the end result of days of research on the physical characteristics of printers, the theory behind printing and ink, the concepts of DPI and PPI, etc. The real question is, how does it stack up against empirical evidence? Does it withstand the test of reality?

In this small study, I'll be looking at whether digital can really compare to film when it comes to significant enlargements, and whether maximum quality can be obtained when upscaling for extremely large format prints. It has long been held that film holds a significant advantage in this area, however I believe that digital is just as capable as film when it comes to printing significant enlargements at high PPI.

The Subject

For this particular study, I will be working with a shot of a giant moth. The fine details visible in this moth, particularly the eyes, make it a good subject for exploring upscaling and sharpening for print.

In the articles above on the visual acuity of the human eye, and the average viewing distances, it was noted that as the viewing distance increases, the print resolution can be reduced without any noticeable loss of detail. While this is true, it makes the assumption that a viewer of a large print will indeed observe it at the expected distance. In practice, however, the assumed viewing distance is not guaranteed, and many a viewer steps in for a closer look, often expecting to see more detail. Achieving the maximum detail in a large print can be important in producing a print that will, quite literally, draw your viewers in.

Sharpness

When viewing a photograph, the detail of a photograph is often lost due to the way it was processed or obscured by imperfections in the way it is filtered and rendered. One of the key aspects of detail is sharpness. Ideal sharpness is perceived when acutance (the definition of edges between areas of perceptible contrast) and resolution (the distinction between closely spaced fine details) are high. The various kinds of processing applied to a digital photograph, from passing through an anti-alias filter by in-camera processing, to scaling an image up in Photoshop, can all affect the sharpness of an image. A variety of methods exist to improve the sharpness of an image, and at lower resolutions, they can be quite effective. The real challenge arises when you need to maintain the maximum level of detail in an image during extreme enlargements.

Data in the detail

When scaling of an image up by any significant degree, say more than double its native size, you often suffer from information anemia and information fabrication defects. The more resolution your native image has, the more leeway you have, however enlargements beyond 2x will usually introduce some degree of softening, loss of detail and artifacting. Image enlargements are usually achieved increasing the resolution of an image up and applying some kind of scaling filtration, such as nearest neighbor (which produces blocky, pixelated images) or bicubic (which smooths out the differences between enlarged pixels.) Image detail is usually preserved by applying some kind of sharpening filter, such as an unsharp mask, which attempt to artificially improve the acutance of an image by hardening the edges softened by bicubic (or possibly more advanced scaling filtration.)

The Test

Both scaling filtration and sharpening try to "preserve" detail by fabricating information. Only an original image at its native size will contain "real" information, and any enlargement will contain a combination of real and fabricated information. Doubling the size of an image effectively doubles the number of pixels, however data stored in those extra pixels can only be generated and approximated from the original image. Bicubic filtration "fills in" extra pixels by fabricating information from nearby original pixels. Sharpening filtration simulates high acutance by lightening lighter content and darkening darker content along edges. Both processes are limited and imperfect mathematical algorithms that can introduce various kinds of undesirable artifacts into an image when they encounter something that falls outside of the domain of the algorithm.

In this test, I'll be comparing various common forms of image upscaling techniques. The most common form of image enlargement is the Bicubic upscale, which is often followed by an Unsharp Mask filter. A variety of third-party scaling tools exist these days, such as Genuine Fractals, PhotoZoom, etc. These tools employ more advanced algorithms including fractal and S-Spline scaling, in combination with unsharp masking, to produce some impressive upscaling results when compared to Bicubic. Despite their high tech nature, a very simple trick can be employed to produce the best results without any need for fancy algorithms or special sharpening post-scale: stepped bicubic scaling.

The sample images used below were scaled up from an original 12.1mp image of size 4272x2848 pixels. At 300ppi, the original image could generate a 14.24"x9.49" print without any scaling (which is a nearly-ideal size to print with an adequate border on 13x19" A3+ paper.) The test will scale the original image enough that it could print a borderless 36"x24" print at 300ppi. This is an upscale of 2.5 times over the original size, which is enough to demonstrate the differences in scaling and sharpening techniques.

NOTE: The sample images below are identical crops at 33.3% of native size. This provides an ideal example of what the image would look like when printed at 300ppi, when viewed on a 100dpi or 96dpi screen (i.e. most professional 30" screens). On a 72dpi screen, the images will be a bit larger than they would appear in print, however they should still be adequate to compare sharpness and get a general idea of print quality.

NOTE: To properly compare the sample images below, its recommended that you save a copy of each image to a single folder on your hard drive, and use an image viewing application (Such as Windows Photo Viewer in Windows 7) to move forward and backwards through two samples to observe the sharpness differences. This should keep the images in an identical position on your screen, making fine detail differences easy to identify.

Bicubic Scaling

The obvious starting point is bicubic scaling. This is the Photoshop default and de-facto standard way most people scale their images in most cases. It can provide good results when the ability to view maximum detail is not a concern, and is generally more than adequate for most upscaling.

To compensate for the softening caused by Bicubic filtering, an unsharp mask is often applied to improve the acutance of fine details. Use of a sharpening filter is often the best approach to improving detail in an upscaled image for 2x or lower enlargements, as well as for downscaling. When performing significant enlargement of several times or more, algorithms that sharpen by trying to enhance acutance can often do more damage than good. Alternative methods for upscaling will generally be required for extreme enlargements. The sample below was upscaled using Bicubic filtering, with an Unsharp mask of 80%, 1.5 radius, and threshold of 3.

PhotoZoom Pro 3: S-Spline Scaling

Many third-party scaling tools exist that can be used to perform extreme enlargements of digital images. They provide some of the most advanced scaling algorithms available today, and can generally do an excellent job upscaling certain types of images. Many of these algorithms are tuned for certain types of image content, and are not ideal for any kind of image. PhotoZoom's S-Spline scaling is adept at identifying high contrast edges where acutance enhancement is most beneficial and crisp, smooth definition is important. It is capable of preserving smooth edge detail through considerable enlargements. Similarly, Genuine Fractal's fractal scaling is also adept at maintaining geometric structure through the use of fractal compression and interpolation.

No single algorithm is ideal, however. S-spline scaling has the tendency to pass over finer details in its quest to perform ideal geometric enlargement, and can often flatten areas of lower-contrast detail. Genuine Fractals has similar problems with detail, however given that it is based on a fractal algorithm, is better at preserving some fine detail at the cost of not being quite as adept at geometric perfection as S-spline scaling is. These tools can be superb when used with the proper kinds of images, such as architecture or images that intrinsically have minimal low-contrast detail and/or many important geometric content.

Stepped Bicubic Scaling

Neither bicubic filtering, nor alternative filtering algorithms such as Lanczos, S-spline, fractal, etc. are capable of preserving maximum detail to any size. The greater the difference between the original size and the destination size, the more information must be fabricated to "fill in the holes", so to say. A simple logical conclusion to this problem, when one takes the time to ponder it, is to reduce the difference. Scale an image from its native size to your desired destination size in discreet steps that are a fraction of the difference between the native and destination.

To take our sample image, scaling from 14"x9" to 36"x24". Performing a direct Bicubic upscale would increase the image size by 252% in both dimensions. Content would need to be generated to fill in 65,593,344 pixels out of 77,760,000 pixels from the 12,166,656 pixels worth of original image data. That is over 84% of the upscaled images total area, a hefty cost and a considerable drain on image detail. The vast majority of the image would be purely fabricated content.

Alternatively, the image could be scaled up in stages, say 10% at a time. The benefit of such an approach is that, for each step, you generate a small amount of new content from a bulk of existing content. Each subsequent step only needs to generate 17.35% of the new image, rather than 84%, and each step has much more accurate information to work with when generating content.

Scaling our original 12.1mp 4272x2848 image by 110%, we generate 2.5 million new pixels for an intermediate 14.7mp 4699x3132 image. Repeat this 110% scaling, and we generate 3.1 million new pixels for a second intermediate 17.8mp 5169x3446 image. Continue scaling until you reach (or surpass) your target image size. If surpassed, one additional downscale to the target size is necessary, however this usually has a negligible (and often positive) effect on the overall sharpness of your image. The sample below was scaled up by 110% ten times to 11080x7386 pixels, then scaled back down to 10800x7200 pixels. A whopping 77.8 megapixel image. No sharpening of any kind was applied to the final result.

Comparing the above sample to the original direct Bicubic example, and there is a noticable difference in sharpness of fine details. Most notable is the highlight in the eye. This scaling is comparable to the second Bicubic example with the ample Unsharp masking applied. It is also comparable to the PhotoZoom S-Spline scaling, however there are some slight improvements in the stepped upscaling over the S-Spline scaling. This concept is scalable itself, however, and more detail can be preserved by scaling up in smaller steps. The sample below was scaled up by 105% twenty times in a row to 11334x7556, then scaled back down to 10800x7200.

Comparing the 5% stepped sample to the direct Bicubic with sharpening or S-Spline scaling, a significant and noticeable improvement can be seen in the 5% stepped version. A considerable amount of detail was preserved by generating less new content in smaller amounts in series. The concept can be pushed pretty far, using 3% increments or even 1% increments, however there are diminishing returns for exponentially greater workload.

Final Conclusion

While it has long been held that film has a considerable edge over digital when printing significant enlargements, I believe that is an old misnomer that can be empirically tested and put to rest. As with digital enlargements, film enlargements are still ultimately fabricating information when scaled beyond their original size. With film it is often easier to bring out fine details (and fine imperfections) that exist and make them more prevalent in an enlarged image, however on a size-comparable basis, film doesn't ultimately contain significantly more original information than digital. Obviously shooting with a larger film format captures more original data, however significantly enlarging a 4x5 slide to 55x36 is not a whole lot better than enlarging an 18mp digital photograph to 55x36. On the flip side, with digital, you may actually have more options at your disposal for preserving detail during significant enlargement than you do with film, and careful massaging of your original pixel data can produce some incredible results. (As a side note, huge enlargements of film are usually done by scanning the image first, and digitally scaling up anyway.)

While performing this test, a single enlargement of the original image was made by scaling it 5% at a time until it reached 55"x36". The image was a whopping 16500x11003 pixels in size, or a monstrous 181 megapixels, some 386% larger than the original image! The image was compared to a direct Bicubic version as well as a Bicubic with Unsharp masking. The stepped scaling preserved at least as much detail as the sharpened version, without the tonal flattening of low contrast detail or harsh edging to fine details. Examples of all three versions below (direct bicubic, bicubic w/ sharpening, staged 5% scaling):

A 55" enlargement is a huge size, and maximum detail can easily be preserved in a digital image for printing at such sizes. Prints of 50-55" are fairly popular amongst experienced landscape photographers, and a landscape photograph looks truly superb when framed and wall mounted at such sizes. So for all you digital photographers out there who have heard for years that you can't get a high-quality super-enlargement with digital, here's to proving the nay-sayers wrong. ;)

It is very important to increase saturation in photo editor before printing. Paper prints always look less bright than what you see on the screen. If you are using Photoshop, set saturation somewhat unnaturally high, and on paper you will get naturally looking colors. Some colors, e.g. blue, are particularly tricky. You can play around with the tricky color saturation and brightness to get them right.

To save on test print costs, generate many small test versions of the same photo, print, choose the best, and only then print it full size.

The most important aspect is good input. Poor quality image = poor quality print. After that one aspect that has been overlooked so far here is colour management.
ICC profiles for the specific printer driver, printer, ink and paper combination can make a huge difference to the image quality reproduced in a print.
As an linux Ubuntu user I was having no luck with printing at all, especially as I was using unbranded inks and low / mid priced papers. Generally printouts were dark, muddy messes and colour shifted with reds being a real problem. Buying a second hand spectrometer and spending a couple of years messing with it has resulted in a profiling method that offers prints of far superior quality.

Instrument:

Gretag-Macbeth (now X-Rite): i1pro spectrometer

Software used:

1. Ubuntu 20.04.2 (Cups 2.3.1-9)
2. Argyll 2.01
3. Gutenprint 5.3.3-4
4. Gnome color manager 3.36.0-1

I have made a much fuller answer here on the askubuntu stack exchange as the method is software specific.