scratch and dig numbers

Figures of merit for the surface quality of an optical component, such as a lens or prism. The processes by which lenses are made inevitably leave imperfections. “Digs” are pits.

A scratch-and-dig evaluation of an optical part addresses two concerns. One is cosmetic. A manufacturer would find it hard to sell a camera lens with a visible scratch on the front objective, even though the scratch had no noticeable effect on photographs. The second is functional. By scattering light these imperfections can, for example, lower the contrast in a photographic image or even, if the light source is a high power laser, damage the equipment.

By U.S. military standards

In the United States, since 1954 optical surface quality has usually been described following military standard MIL-PRF-13830B and its predecessors. The rating is formatted as two numbers separated by a hyphen, or sometimes a slash, for example 80-50. The first is the scratch number and the second the dig number.¹

The dig number is the diameter, measured in hundredths of a millimeter, of a circle which would enclose the biggest dig in the surface.

Dig numbers are the actual diameters of defects allowed, specified in units of 1/100mm. In the case of irregular shaped digs the diameter shall be taken as the average of the maximum length and maximum width.²

So, if a lens surface is rated 80-50, somewhere on that surface is a pit 0.5mm in diameter, about half a pinhead. The standard only allows one dig of the stated maximum size per 20mm of lens diameter, and there are additional constraints, such as that if the dig number is 10 or less, every dig edge must be at least 1 millimeter away from the edge of its nearest neighbor. Bubbles are treated as digs.

The scratch number is a less objective measurement. It is arrived at through a method similar to the one machinists use to rate the smoothness of a machined surface, by visual comparison to a set of calibrated samples.³ MIL-PRF-13830B describes dark-field lighting conditions under which the part being evaluated is to be viewed together with working scratch standards. The evaluator picks the best match, essentially matching the brightnesses of the two surfaces by eye. Because of the nature of the visual matching procedure, it is possible for different evaluators to assign different scratch numbers to the same part. The MIL standard includes other requirements, such as that the combined length of the biggest scratches can't be more than ¼ the diameter of the lens. But the scratch number is not a direct measurement of any dimension of the scratches, but of scratch visibility.

The scratch standards are described in U.S. Army ARDEC drawing “Surface Quality Standards for Optical Elements (scratch and dig) Drawing C7641866.” (Revision R, as of 2010). The actual prototypes are kept at the Picatinny Arsenal in New Jersey. For each scratch number (80, 60, 40, 20, 10) there is a pair of prototypes, one defining the maximum allowable visibility for that scratch number and another defining the lowest allowable visibility.

The military and its vendors can refer to these prototypes, or to working standards directly calibrated against them. Everyone else must rely on commercially available copies of the prototypes, a set of which costs several thousand dollars. Working standards from commercial suppliers differ slightly from maker to maker, so it is a good idea to include in a surface quality specification the name of the manufacturer of the working standards to which the part is to be compared.

Some examples of ratings appropriate for various uses:

80-50 cosmetic. Elements far from the image plane.
60-40 many commercial lenses
40-50 central zone of military eyepieces
40-20 Low power lasers.
20-10 Medium power lasers. Central area of high-quality eyeglasses.
10-5 Research with high power lasers.

Another military standard covered the surface quality of the coating of optical parts.⁴ For transparent coatings, the standard applied the method and two-numeral designation of the MIL-0-13830 standard. But for opaque coatings, it adopted designations consisting of “two letters separated by a hyphen.” Dig letters were defined as follows (sec.

Dig letter A B C D E F G H
Diameter in mm 0.05 0.10 0.20 0.30 0.40 0.50 0.70 1.00

Scratch letters were defined as follows (sec.

Scratch letter A B C D E F G
Scratch width (microns) 5 10 20 40 60 80 120

In this case, unlike MIL-PRF-13830B, the actual width is being used to characterize a scratch. The standard states:

The length and width of scratches, and the dig (hole) diameters shall be determined by use of interferometry, microscopic measuring devices, calibrated precision comparators, or similar applicable precision measuring devices. The width, length and density of all scratches in the coating shall conform to the requirements of⁵

In other words, the resulting rating can serve functional, and not just cosmetic, purposes.

1. Performance Specification. Optical Components for Fire Control Instruments: General Specification Governing the Manufacture, Assembly, and Inspection of. (MIL-PRF-13830B, 9 January 1997). Section, Designation of defect size..

2. Section, Dig designation.

3. Some suppliers of optical parts give a scratch number which is the maximum scratch width in microns. This usage does not conform to the MIL-PRF-13830B standard. Such suppliers will usually state on the page with the part's specifications that that is how they are defining scratch number. In 1954, Revision H of Drawing C7641866 said the scratch number was the width in microns. Two years later Revision J indicated the scratch number was the width in tenths of a micron. This sowed confusion, but the mil standard and the prototypes at the Picatinny Arsenal remained unchanged; i.e., the standard remained a visibility standard, not a width standard.

4. Coating, Single or Multi-Layer, Durability Requirement for (MIL-C-48497A, 8 September 1980). See and The standard was inactivated for new design on 14 March 1997.

5. MIL-C-48497A, section Opaque coated surfaces.

By ANSI/OEOSC standard OP1.002

In 2000 efforts began to draft a voluntary American National Standard that would serve most of the purposes of the military standards. The standard was first issued in 2006, with the first revision in 2009. One of the useful features of this standard is that it offers a choice of methods, one for cosmetic purposes and a dimensional one for functional purposes. The cosmetic one is a cleaned-up version of MIL-PRF-13830B, using the same two-numeral designation and relying on the same Picatinny prototypes, but removing ambiguities and clarifying the testing procedures. For scratches, it is a visibility standard, and subjective.

The dimensional method uses letters instead of numbers in its notation, so it is immediately obvious that the dimensional method is intended. The letters and their values are taken from MIL-C-48497A; the standard provides an easy transition for anyone previously using the military standards. Actual measurement of the dimensions of a scratch is required.

A feature not available under the military spec is that specifications are not limited to the pre-defined maximums, but can be any value — just follow the letter “A” with a number. For example, “F-F” would be a functional equivalent to the cosmetic “80-50”, but “A45-A350” would call for scratch with a maximum width of 45 microns and digs with a maximum diameter of 350 microns. In practice, this feature is most likely to be used to specify scratch widths smaller than 5 microns.

scratch width
in microns
dig diameter
in microns
(not .01 mm)
120 700 G
80 500 F
60 400 E
40 300 D
20 200 C
10 100 B
5 50 A

1. ANSI/OEOSC OP1.002-2009. American National Standard for Optics and Electro-Optical Instruments — Optical Elements and Assemblies — Appearance Imperfections. The ANSI standard may be purchased here this link goes to a new page.

By ISO standard 10110-7

In 1996, the ISO issued standard 10110, which was basically taken from the German standard DIN 3140. It has since been adopted as a national standard by Germany, Japan, France, Russia and other nations, and is used in many others, including increasing numbers in the U.S., notably for the National Ignition Facility. At the time of writing, the most recent version was ISO 10110-7:2008.¹

One of the ways the ISO standard differs from those discussed above is the way it categorizes surface defects. The very concepts of scratches and digs are closely related to the historical process of grinding lenses with abrasives. The ISO standard instead approaches the problem strictly from the perspective of dimension. Instead of digs, the category “localized surface imperfections” includes not only digs but also any scratch shorter than 2 millimeters. Longer scratches then fall into the category “long scratches.” The square root of the total defect area for a region is the grade number for that region.

Under this standard, a specification of surface quality takes the form:²

5/X × Y;LZ × F

for example, 5/1 × 0.05;L5 × 0.004

The “5” is a header indicating that this is a designation of surface quality. The “L” is another header; it identifies the part of the designation that deals with “long scratches.” The other elements are as follows:

X is the maximum number of digs the part can have at the dig size specified by Y.

Y is the maximum dig size, in millimeters.³

Z is the number of scratches

F is the width of the widest scratch, in millimeters The available grade numbers are 0.004, 0.006, 0.010, 0.016, 0.025, 0.040, 0.060, 0.100, 0.160, 0.250, 0.400.

At the time of writing (summer 2010), the U.S. is in the process of adopting as an American National Standard (ANSI/OEOSC OP 1.110), a modified version of ISO 10110. Among other slight differences, it is likely to permit the (optional) use of military standards.

1. ISO 10110-7:2008. Optics and photonics — Preparation of drawings for optical elements and systems — Part 7: Surface imperfection tolerances. It can be purchased here this link goes to a new page. See also ISO/DIS 14997. Optics and optical instruments — Test methods for surface imperfections of optical elements.

2. The earlier versions of the standard also described a second method which lead to a simple accept/reject decision. That method was dropped in 2008.

3. In the ISO standard the same letter is assigned to different variables, which are then distinguished by adding prime marks (e.g., N′, N″, N′′′). This practice has confused some readers. An actual specification does not include any prime marks.

for further reading

David M. Aikens.
The truth about scratch and dig.
Optical Society of America, Optical Fabrication and Testing Technical Digest (2010).
Available on the web at this link goes to a new page

Matthew Young.
The scratch standard is only a cosmetic standard.
pages 185-190 in
John E. Greivenkamp and Matthew Young, editors.
Surface Characterization and Testing II (Proceeding Volume).
Proceedings/ SPIE--the International Society for Optical Engineering, vol. 1164.
Bellingham, WA: SPIE, 1989.

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