Grating Prisms (GRISMS)

A grism (or Carpenter's prism) is formed by replicating a transmission grating onto the hypotenuse face of a right-angle prism. Grisms are useful in spectrometers that require in-line presentation of the spectrum. The light diffracted by the grating is bent back in line by the refracting effect of the prism (see Fig. 1). The dispersion of a grism is not linear, since the dispersive effects of the prism and grating are superimposed.

Ray path of a grism in its usual configuration for the in-line wavelength. Light is incident normally on the back face of the prism, is refracted at the interface between the prism (glass of index n) and the resin (index nE) and then diffracted at the interface between the resin and the air (the grating surface).

Figure 1.GN – grating normal; Z – zero order of prism; A = apex angle of prism; D = deviation angle between Z and in-line diffraction direction; θ = blaze (groove) angle of grating.

In-Line Transmission

The grating equation for diffraction through a grism is

mλ = d (n sinα + sinβ) (1)

where n is the refractive index of the glass. [We assume that the index nE of the resin is equal to n for wavelength λ.] For in-line diffraction, the angles α and β must have opposite signs since they lie on opposite sides of the grating normal (see Fig. 1). Moreover, for in-line transmission, we see from the figure that

α = –β = θ = A (2)

where A is the apex angle of the prism, so

mλ = d (n –1) sinθ (3)

from Eq. (1). Since θ = A, the apex angle A that provides in-line diffraction for wavelength λ in order m is given by

sinA = mλ / (d (n –1)) (4)

The assumption that nE ≈ n for wavelength λ is not likely to be true in most cases, though the resulting error in Eq. (4) is quite small.

Designing a GRISM

The five steps used to design a grism are listed below.

  1. Select the prism material desired (e.g., BK-7 glass for visible light or fused silica for ultraviolet light).
  2. Obtain the index of refraction of the prism material for the in-line wavelength.
  3. Select a grating constant d for the appropriate dispersion required. Determine the apex angle A from Eq. (4).
  4. To maximize the efficiency of the in-line wavelength, select the grating from the Diffraction Grating Catalog with the groove angle θ closest to the apex angle A.
  5. If the prism apex angle A is specified initially, then the groove spacing d is determined by Eq. (4). This restricts the range of dispersions available to the designer.
Figure 2. Index of refraction vs. wavelength for the two types of replica resins as well as the two common substrate materials (BK-7 and fused silica).

Littrow Reflection GRISMS

The reflection version of the transmission grism is often used in miniature Littrow spectrographs for wavelength demultiplexing using fiber optics (see Fig. 3). A gradient index lens (or "grin" lens) usually performs the collimating function and the prism transmits the light to the grating.

Figure 3.

The apex angle A should be close to the groove angle θ to achieve maximum efficiency. The nominal blaze wavelength of a grating found in the Diffraction Grating Catalog must be multiplied by the refractive index nE of the replica resin, since diffraction takes place inside the resin rather than in air.

Ordering GRISMS

Any of the suitable gratings listed in the Diffraction Grating Catalog can be replicated to form grisms. Please contact us for price quotations.

Download Diffraction Grating Catalog
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