Introduction

Digital preservation projects typically require that materials be imaged at a “Best Practice” standard of either 300 or 600 pixels per inch (ppi) for actual-size representation, often without a clear understanding of why or how these rigid guidelines are important. Digitizing large quantities or oversize materials can be overly demanding of staff and resources in many cases. There are opportunities for using a lower, more manageable ppi and there are situations when a very high number of ppi is necessary.  To ensure overall project success, it is important that the choice of ppi be a rational and informed one.

The following article includes some helpful advice for understanding how to calculate sample frequency / ppi based on need. At a glance, the formulas may seem complicated, but rest assured, the math is actually quite simple. The sections that follow begin with a brief review of terminology, followed by an overview of an approach for determining ppi needs, a case study in which 300 ppi is preferred, and some additional considerations.

Terminology

Pixels (picture elements) are the fundamental units of digital image files. They are arranged in a grid and vary in brightness and/or color.

Pixel size varies and is a characteristic of imaging devices as well as electronic image files. A 33 megapixel digital camera back might have pixel sizes of 7.2 x 7.2 microns while a graphics LCD might have a pixel size of 127 x 127 microns. Image file pixel sizes are determined by sample frequency, which is established within imaging device driver software or image editing programs. The relationship of device pixels to image file pixels is somewhat similar to that of film grain to photographic enlargements and projected film.

Sample frequency is usually expressed as pixels per inch (ppi), the number of pixels within one inch of the width or the height of an image file. The term “resolution”, the ability to distinguish detail, is commonly misused to refer to sample frequency. For readability and clarity, this paper employs “sample frequency”.

Pixel Dimensions refers to the number of pixels in the length and width of an image file.

Megapixels generally refers to the total number of pixels an imaging device can record: the product of multiplying the number of pixels in the length of a device’s potential image file by the number of pixels in its width. Megapixels is commonly used in marketing for digital cameras and rarely used for describing image files.

A very basic approach

Examine the details closely. Determine the smallest element to be recorded and measure its smallest dimension. If it’s a mark from a technical pencil, its width might be between .0118 and .063 inches (standard technical pencil lead sizes).

Divide 1 by the smallest element’s smallest dimension (in inches) to determine the number of details that would fit side-by-side into an inch. Round the quotient up in order to convert to pixels per inch. The number of technical pencil marks that would measure up to 1 inch is between 84.74 and 15.87; the absolute sample frequency for recording any of them is between 85 and 16 ppi.

1  / .0118 inch  =  84.74 details / inch  =  85 ppi

1  / .063 inch  =  15.87 details / inch  =  16 ppi

PPI, practical sample frequencies, and extended usefulness

In the illustration to the left, the letter “e” measures ten pixels wide. If twenty pixels span one inch of the image file’s entire width or height, its sample frequency is expressed as 20 ppi and the letter “e” is determined to be ½ inch wide.

“Lines per inch” is an extension of pixels per inch where a line represents a row or column that is one pixel wide. The 20 ppi file’s image could portray 20 horizontal or vertical lines per inch.

Without variation in tonality or color, 20 side-by-side lines would display as an amorphous mass. For this reason, we use alternating black and white lines (line pairs), which are traditionally used in evaluating the resolving power of optical systems. To better represent detail with pairs of lines or pixels, 40 ppi is used for recording the letter “e” and for our small pencil mark, a minimum sample frequency of 170 ppi.

The problem of “scattered pixels” provides an argument for using twice the minimum sample frequency for representing discernible diagonal line pairs. Pixel-wide vertical and horizontal lines are more easily represented than pixel-wide diagonals. Regardless of capture / scanning device capabilities and limitations, minute details are vulnerable to a degree of aliasing or pixel scattering during capture and processing phases.

The top left illustration shows a potential effect of rotating an image file. Although the lines can (arguably) be discerned, there are not enough pixels for well-defined edges.

The top right illustration’s line pairs were captured with a practical sample frequency of twice as many pixels per inch. Some tools (Adobe Photoshop, ImageMagick, etc.) are very good at resampling for basic image manipulations such as rotation. However, there is no way to guarantee which applications will be used in future work with the image file. Providing the smallest important details with two or more pixels instead of one is a good rule of thumb for ensuring readability. When doubling, multiply the minimum sample frequency by 2.

A review

Absolute sample frequency: one pixel or line represents one image detail

Minimum sample frequency: two pixels or lines represent one image detail

Practical Sample frequency: four pixels or lines represent one image detail

Theory into practice: A case for 300 ppi

An image file with readable markings was the primary goal for digitizing the blueprint illustrated to the right. Markings indicated by the red circles suggest the scale of typical important details. The lines smallest dimensions measured .014 inches, requiring an absolute sample frequency of close to 75 ppi. At a minimum sample frequency of 150 ppi, line edges were better defined, improving legibility and the overall appearance of the image. The sample frequency was further doubled to a practical 300 ppi, safeguarding against aliasing and extending the usefulness of the image file.

Doubling the minimum sample frequency introduced a second level of information, which included minor paper damage and a suggestion of paper texture. The final representation of the .014 inch line was 3 to 4 pixels wide. At 150 ppi, the same line would have been recorded with a width of only 1 or 2 pixels. The 300 ppi image file can be resized or downsampled as needed; greater detail, however, can only be achieved by re-digitizing the blueprint, subjecting it to more handling and harmful light exposure.

Tables

The following tables provide sample frequencies for detail sizes in inches and millimeters.

Minmum sample frequency / ppi	Practical sample frequency / ppi	Dimension of smallest recorded detail
36 ppi	72 ppi	1/18 inch
72 ppi	136ppi	1/36 inch
100 ppi	200 ppi	1/50 inch
150 ppi	300 ppi	1/75 inch
200 ppi	400 ppi	1/100 inch
300 ppi	600 ppi	1/150 inch
400 ppi	800 ppi	1/200 inch
600 ppi	1200 ppi	1/300 inch
800 ppi	1600 ppi	1/400 inch

Minmum sample frequency / ppi	Practical sample frequency / ppi	Dimension of smallest recorded detail
36 ppi	72 ppi	1.42mm (1.411mm)
72 ppi	136 ppi	.71 mm (.705 mm)
100 ppi	200 ppi	.51 mm (.508 mm)
150 ppi	300 ppi	.34 mm (.339 mm)
200 ppi	400 ppi	.26 mm (.254 mm)
300 ppi	600 ppi	.17 mm (.169mm)
400 ppi	800 ppi	.13 mm (.127 mm)
600 ppi	1200 ppi	.09 mm (.085 mm)
800 ppi	1600 ppi	.07 mm (.064 mm)

Putting the details into greater perspective: when too much is not enough

Consider scans / captures made at 300 ppi. The smallest recorded detail could measure .007 inches (about half the width of a fine technical pencil mark). Sometimes it is important to record information of that scale: for example, in the case of object damage (staining, cracking, etc.) where the damage will be visually analyzed. However, a 300 ppi scan / capture does not come close to recording detail on the scale of paper fiber.

Typical paper fiber widths range from 15 micrometers to 30 micrometers. A conservator wishing to record details of this scale, for a digitized A4-size object, would ask for a file size of 14,069 pixels by 19,832 pixels, based on the following:

• detail measurements of 15 micrometers to 30 micrometers
• minimum sample frequency of 1,695 ppi to 3390 ppi
• image file dimensions of 14,069 pixels by 19,832 pixels; a 16-bit file size of greater than 1.5 gigabytes

For recording paper fiber-scale detail, a very strong case can be made for capturing a portion of the object at very high magnification or for waiting a few years for imaging technology to catch up with demand.

Additional considerations

Performance and resolution

Lens or optical issues and device performance factor into the resolution of digitizing systems. Since the aim of this article is to provide a basic understanding of how and why sample frequency is considered in digital reformatting, lengthy discussions of the impact of lens resolution and approaches for compensating have regretfully been sidestepped. It is important to note that the ability to record detail is also dependent on the quality of the optical systems employed.

Recording texture

Lighting is an important contributor in recording detail for textured and three dimensional objects. Using a very high sample frequency will not always provide satisfactory detail. Nuanced lighting is often necessary for revealing textures and details that might be lost with the uniform illumination of flatbed scanners. The complexities of successful lighting for photography are within the domain of a skilled and experienced photographer.

Preserving edges

Image borders are often an unavoidable necessity for archival imaging. Since perfectly square objects are a rarity, uniform image borders are often tolerated for the sake of preserving object shape and edge detail. When incorporating borders, sample frequency may need to be adjusted for digitization projects where pixel dimensions are a determining project guideline.

Conclusion

When selecting materials and establishing guidelines for a digitization projects, the details must not be overlooked. It is important to examine the materials, to identify the smallest information that needs to be recorded, and to determine sample frequency case by case. For many projects, 300 ppi or 600 ppi makes perfect sense. There are situations in which lower resolution is appropriate. If the project merits it, there are techniques for achieving much higher resolution as well. For any digitization project, a basic understanding and appreciation of sample frequency is essential for making the most practical, informed decisions when establishing guidelines.