How to Specify Substrates

Material

The first decision is the choice of the substrate material. It should be free of absorption for all wavelengths of high transmittance. If no transmittance occurs, a low-cost material can be used, e.g. Borofloat^® (SCHOTT AG), for metallic mirrors. With respect to the surface form tolerance, a low thermal expansion is beneficial.

Shape

The shape must be specified for both sides separately. All combinations of plane, convex and concave surfaces are possible. This is also the case for wedges, e.g. 30 arcmin, which can be applied to any kind of surface, plane as well as convex or concave. For curved substrates there are different conventions for the sign of the radius of curvature. Sometimes “+” means convex and “-” means concave. Other users refer to the direction of light propagation. In this case, “+” means “curvature in the direction of propagation” and “-” means “curvature against the direction of propagation”. Please specify concave or convex in words or using the acronyms CC or CX to avoid confusion.

Size

The main decision should be about the size of the substrate, i.e. edge length or diameter. Small diameters are more favorable for production. The sagitta heights become lower, so it is easier to achieve a good form tolerance. Although often denoted otherwise in optical designs, LAYERTEC specifies the thickness as the maximum thickness of the substrate, i.e. the center thickness for plano-convex substrates and the edge thickness for plano-concave substrates. Consequently, the thickness of a wedged plate is measured on the thicker side.

In order to achieve a good form tolerance, the ratio of diameter and thickness should be considered. As a rule of thumb the thickness should be at least one fifth of the diameter. Of course, other ratios are possible but production costs and therefore prices increase as well.

Tolerances

Besides size and material, the tolerances are most important for manufacturing costs and thus pricing. Of course, the optics must fit into the mount, so the diameter should not be larger than specified. Thus, the most common specification is Ø = X mm (+0 mm/-0.1 mm). In contrast, the thickness is generally free in both directions. LAYERTEC usually specifies it with a tolerance of ±0.1 mm. There is a lot of confusion about the specification of wedge, parallelism and centering. Please note that wedge and parallelism describe the angle between the optical surfaces while centering describes the angle between the optical surfaces and the side surfaces. LAYERTEC standard substrates have a parallelism better than 5 arcmin. Specially made parallels may have a parallelism lower than 10 arcsec. Standard wedged substrates have wedges of 0.5° or 1°. Larger wedge angles are possible depending on the substrate size. In general, the 90° angle between optical and side surface has a precision of 20 arcmin. Centering is an additional optics processing step which improves this accuracy to a few arcmin.

Curved substrates can be described using the same nomenclature. It should be distinguished between mirrors and lenses. The side surfaces of mirror substrates are parallel. Nevertheless, the direction of the optical axis can be inclined with respect to the side surfaces. After centering, the side surfaces are parallel to the optical axis.

Surface Form Tolerances

The surface form tolerance is usually measured by interferometers and is specified in terms of the reference wavelength (λ = 546 nm if not otherwise stated). In order to avoid confusion, it is necessary to clearly distinguish between flatness, power and irregularity. In the following, flatness and irregularity shall be explained for a plane surface. Generally speaking, every real surface is more or less curved. Imagine that the “peaks” and “valleys” of a real surface are covered by parallel planes (see Fig. 2). The distance between these planes is called the flatness. This flatness consists of two contributions. The first contribution is a spherical bend of the surface, which may be described by a best fitted sphere to the surface. With respect to an ideal plane, the sagitta of this curvature is denoted as power. This spherical bend does not affect the quality of the reflected beam. It just causes a finite focal length. The second contribution is the deviation from the best fitted sphere, which is named irregularity. This is the most important value for the quality of the beam.

The standard ISO 10110 provides a sufficient method for specifying the surface form tolerance. Having the best comparability with the measurement results, all values are specified as numbers of interference fringes, with 1 fringe = λ/2. In technical drawings according to ISO 10110, the surface form tolerance is allocated as item number 3/: 3/ power (irregularity)

Example: A slightly bent (λ/4) optics which is regular (λ/10) would be specified as follows:

• 3/ 0.5 (0.2)

Using the optics only for transmittance (e.g. laser windows), power as well as irregularity do not matter. A transmitted beam is not affected if the optics has the same thickness all over the free aperture. The influence of thickness deviations on the transmitted beam is defined in a similar way as the flatness. It is also measured in parts of the reference wavelength and called “transmitted wave front” (13/). For instance, the window in Fig. 2 has a flatness of λ/4 but a transmitted wave front of λ/10.

Coating Stress

Thin substrates cannot withstand the coating stress. The coating will cause a spherical deformation (for rotationally symmetric coatings). This means that a finite sagitta or power occurs. In case of circular substrates, the irregularity is not affected by this issue. Even if power deviation is considered, the quality of a beam under normal incidence is not affected.

Defects

ISO 10110 is an international standard for the description of optical elements. According to ISO 10110, maximum permissible surface imperfections can be specified as item number 5/ in technical drawings. It allows for dimensional as well as visibility specification of surface imperfections, the latter being based on the MIL-O-13830 standard.

In the visibility specification, scratches and digs have to be distinguished. The scratch number refers to the visibility of the biggest scratch compared to the corresponding one on a norm template. “10” is the smallest scratch on this template. Thus, better qualities cannot be specified legitimately. Moreover, the visibility specification does not specify a directly measured but an apparent scratch width. The number is interpreted as tenths of a micron or as microns. In contrast, the dig number can be determined easily. The numerical value is equal to the maximum apparent dig diameter in hundredths of a millimeter. One maximum-size dig per 20 mm clear aperture is allowed.

In the numerical specification, the grade number is the side length in millimeters of a square area which is equivalent to the total defect area. So, 1 × 0.025 describes a surface defect area of 625 μm². Additionally, scratches of any length are denoted with a leading L. A long scratch, i.e. exceeding 2 mm of length, with a width of 4 microns would be specified as L 1 × 0.004.

All these explanations are very simplified. For a detailed specification please read the complete text of the relevant standard.

Please Note

There is no direct conversion between visibility and dimensional specification. All specifications in this catalog are dimensional. The mentioned scratch/dig values are rough approximations.