Si24 Directly measure blaze angle in reflection
A typical grating has 3 blaze angles.
The width of the facet is inversely related
to the breadth of the blaze envelope.
Depending on the illumination angle,
some facets are shadowed.
shadowed
✔
✗
What Astronomers want:
-know the realized* R3 blaze angle and its uncertainty
-a small** uncertainty
-no avoidable*** efficiency loss
*the realized blaze angle may differ from the design blaze angle since it depends
intimately on the Si cutting angle (well known) and the anisotropic KOH wet etch
rates (poorly known, variable)
**small means negligible contribution to the overall uncertainty in the alignment of
the spectrograph during integration and testing. Ask Dan Jaffe what X is.
***geometrical efficiency loss comes from groove shadowing, which can be
anticipated in the design.
✗
Immersed in Si
GROOVE TOP SHADOWING MEMO
MICHAEL GULLY-SANTIAGO
1. Introduction
This document describes the geometry of micromachined silicon immersion gratings
being developed at the University of Texas Department of Astronomy Silicon Diffractive
Optics Group and the MIT Nanoruler Group. Specifically, we calculate the acceptable
groove top to pitch length ratio above which the efficiency of the devices is degraded. This
information is useful for the design of gratings using direct writing systems, where the
groove width is a free parameter. Maintaining a large groove top to pitch length ratio is
important to avoid failures during processing, such as undercutting or over etching.
2. Geometry
Figure 1 shows an overview of a silicon immersion grating. Figure 2 shows a detail of a
single groove, chronicling the relevant geometry; the parameters are listed below.
t is the groove top width
p is the groove spacing (also called the groove pitch)
δ is the blaze angle
a is the silicon etch angle; for this document we adopt a = 70.53
◦
,
the maximum allowable ratio of
t
p is given by:
t
p =
1
1 +
tan(a)
tan(δ)
,
So, for the adopted value of a, and tan(δ) = 2 (i.e. an R2 echelle), we have
t
p
∼
= 0.41.
For an R3 echelle, we have
t
p
∼
= 0.51.
References
[Marsh et al.(2007)] Marsh, J. P., Mar, D. J., & Jaffe, D. T. 2007, Applied Optics, 46, 3400
MICHAEL GULLY-SANTIAGO
1. Introduction
This document describes the geometry of micromachined silicon immersion gratings
being developed at the University of Texas Department of Astronomy Silicon Diffractive
Optics Group and the MIT Nanoruler Group. Specifically, we calculate the acceptable
groove top to pitch length ratio above which the efficiency of the devices is degraded. This
information is useful for the design of gratings using direct writing systems, where the
groove width is a free parameter. Maintaining a large groove top to pitch length ratio is
important to avoid failures during processing, such as undercutting or over etching.
2. Geometry
Figure 1 shows an overview of a silicon immersion grating. Figure 2 shows a detail of a
single groove, chronicling the relevant geometry; the parameters are listed below.
t is the groove top width
p is the groove spacing (also called the groove pitch)
δ is the blaze angle
a is the silicon etch angle; for this document we adopt a = 70.53
◦
,
the maximum allowable ratio of
t
p is given by:
t
p =
1
1 +
tan(a)
tan(δ)
,
So, for the adopted value of a, and tan(δ) = 2 (i.e. an R2 echelle), we have
t
p
∼
= 0.41.
For an R3 echelle, we have
t
p
∼
= 0.51.
References
[Marsh et al.(2007)] Marsh, J. P., Mar, D. J., & Jaffe, D. T. 2007, Applied Optics, 46, 3400
Date: May 27, 2009.
1
δ is the blaze angle
a is the silicon etch angle; for this document we adopt a = 70.53
◦
,
the maximum allowable ratio of
t
p is given by:
t
p =
1
1 +
tan(a)
tan(δ)
,
So, for the adopted value of a, and tan(δ) = 2 (i.e. an R2 echelle), we have
t
p
∼
= 0.41.
For an R3 echelle, we have
t
p
∼
= 0.51.
References
[Marsh et al.(2007)] Marsh, J. P., Mar, D. J., & Jaffe, D. T. 2007, Applied Optics, 46, 3400
Date: May 27, 2009.
1
GROOVE TOP SHADOWING MEMO
MICHAEL GULLY-SANTIAGO
1. Introduction
This document describes the geometry of micromachined silicon immersion
being developed at the University of Texas Department of Astronomy Silicon Di
Optics Group and the MIT Nanoruler Group. Specifically, we calculate the ac
groove top to pitch length ratio above which the efficiency of the devices is degrad
information is useful for the design of gratings using direct writing systems, w
groove width is a free parameter. Maintaining a large groove top to pitch length
important to avoid failures during processing, such as undercutting or over etchin
2. Geometry
Figure 1 shows an overview of a silicon immersion grating. Figure 2 shows a de
single groove, chronicling the relevant geometry; the parameters are listed below.
t is the groove top width
p is the groove spacing (also called the groove pitch)
δ is the blaze angle
a is the silicon etch angle; for this document we adopt a = 70.53
◦
,
the maximum allowable ratio of
t
p is given by:
t
p =
1
1 +
tan(a)
tan(δ)
,
So, for the adopted value of a, and tan(δ) = 2 (i.e. an R2 echelle), we have
t
p
For an R3 echelle, we have
t
p
∼
= 0.51.
References
[Marsh et al.(2007)] Marsh, J. P., Mar, D. J., & Jaffe, D. T. 2007, Applied Optics, 46, 3400
Date: May 27, 2009.
1
gully
saltcooky12
takasumasakazu
ailaboocu
gamella
konakalab
lahuuki
lcolladotor
s1ok69oo
trycycle
fixstars
misawann
norihirosuzuki
aki_iinuma
aleyda
maltzj
akosma
searls
colly
akmur
brianwarren
eitanlees
mza
mojombo
jmmastey