Reflectivity from Metal Mirror vs Angle

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Jarvis

Posted: Wed Mar 05, 2008 12:00 am

Guest

I'm trying to model the reflectivity of an planar aluminum mirror vs angle.

Basically, I have a nearly monochromatic, 1.5um beam being steered by a
planar aluminum mirror. Angles of incidence vary from about 25 degrees to
65 degrees. I'm seeing some intensity variation as a function of angle of
incidence. (At least I think I am. The apparatus is actually more
convoluted than my simple description and doesn't lend itself to making the
measurement directly.)

I thought it would be "fun" to see if application of the Fresnel equations
to metal reflectors could accurately describe situation. In particular, I
suspect there would be justification for using a different metal reflector
such as gold. I have plenty of signal with aluminum but my measurement
can't tolerate the variation vs angle. This would be an expensive custom
part, so I would like to have some solid justification.

After digging out Hecht's Optics and reviewing what I needed to do, I
realized that the probability of me making a mistake in the calculation is
pretty high. (Additionally, the only complex index data that I can find is
in the Handbook of Chemistry and Physics for 0.8eV (1.55 um). I presume
this data is close enough.)

Am I proceeding along the right path? I was a bit surprised to not see any
aluminum or gold
reflectivity tabulated vs angle at various wavelengths in the open
literature. (Best that I could come up with was normal and 45 degree
incidence in the Melles Griot catalog.) Seems like there should be an
easier way. Is there a reference somewhere that has this data tabulated?
....or do I just need to "grunt it out" ?

Sincerely,

John

Salmon Egg

Posted: Wed Mar 05, 2008 12:50 am

Guest

In article <jqqdnbW41LOahlPanZ2dnUVZ_tmhnZ2d@comcast.com>,
"Jarvis" <john.jarvis @ yahoo.co.uk> wrote:

Quote:

I'm trying to model the reflectivity of an planar aluminum mirror vs angle.

Basically, I have a nearly monochromatic, 1.5um beam being steered by a
planar aluminum mirror. Angles of incidence vary from about 25 degrees to
65 degrees. I'm seeing some intensity variation as a function of angle of
incidence. (At least I think I am. The apparatus is actually more
convoluted than my simple description and doesn't lend itself to making the
measurement directly.)

I thought it would be "fun" to see if application of the Fresnel equations
to metal reflectors could accurately describe situation. In particular, I
suspect there would be justification for using a different metal reflector
such as gold. I have plenty of signal with aluminum but my measurement
can't tolerate the variation vs angle. This would be an expensive custom
part, so I would like to have some solid justification.

After digging out Hecht's Optics and reviewing what I needed to do, I
realized that the probability of me making a mistake in the calculation is
pretty high. (Additionally, the only complex index data that I can find is
in the Handbook of Chemistry and Physics for 0.8eV (1.55 um). I presume
this data is close enough.)

Am I proceeding along the right path? I was a bit surprised to not see any
aluminum or gold
reflectivity tabulated vs angle at various wavelengths in the open
literature. (Best that I could come up with was normal and 45 degree
incidence in the Melles Griot catalog.) Seems like there should be an
easier way. Is there a reference somewhere that has this data tabulated?
...or do I just need to "grunt it out" ?

Sincerely,

John

I cannot see any way of calculating reflectivity without knowledge
equivalent of knowing the reflecting metal's complex index of
refraction. You must also realize that deposition technique can affect
the complex index. Moreover, it is possible that the index is
anisotropic. Assuming uniform isotropic films, reflectivity calculation
as a function of angle relatively straightforward.

Use a combination of the theory presented by Ramo and Whinnery's "Fields
and Waves in Modern Radio," and the matrix methods presented by Louis
Pipes in Condon and Odishaw's "Hanbdbook of Physics." Some complex index
information is available in OSA's "Handbook of Optics." In all
likelihood, there are more modern compilations of complex index data

Bill

Adam Norton

Posted: Wed Mar 05, 2008 1:20 am

Guest

"Jarvis" <john.jarvis @ yahoo.co.uk> wrote in message
news:jqqdnbW41LOahlPanZ2dnUVZ_tmhnZ2d@comcast.com...

Quote:

I'm trying to model the reflectivity of an planar aluminum mirror vs
angle.

Basically, I have a nearly monochromatic, 1.5um beam being steered by a
planar aluminum mirror. Angles of incidence vary from about 25 degrees to
65 degrees. I'm seeing some intensity variation as a function of angle of
incidence. (At least I think I am. The apparatus is actually more
convoluted than my simple description and doesn't lend itself to making
the
measurement directly.)

I thought it would be "fun" to see if application of the Fresnel equations
to metal reflectors could accurately describe situation. In particular, I
suspect there would be justification for using a different metal reflector
such as gold. I have plenty of signal with aluminum but my measurement
can't tolerate the variation vs angle. This would be an expensive custom
part, so I would like to have some solid justification.

After digging out Hecht's Optics and reviewing what I needed to do, I
realized that the probability of me making a mistake in the calculation is
pretty high. (Additionally, the only complex index data that I can find
is
in the Handbook of Chemistry and Physics for 0.8eV (1.55 um). I presume
this data is close enough.)

Am I proceeding along the right path? I was a bit surprised to not see
any aluminum or gold
reflectivity tabulated vs angle at various wavelengths in the open
literature. (Best that I could come up with was normal and 45 degree
incidence in the Melles Griot catalog.) Seems like there should be an
easier way. Is there a reference somewhere that has this data tabulated?
...or do I just need to "grunt it out" ?

Sincerely,

John

Check out the FreeSnell program:
http://swiss.csail.mit.edu/~jaffer/FreeSnell/

Zemax and other optical design and thin film design programs can also
calculate this.

There will indeed be a significant change in reflectance for s and p
polarization over that angle range for aluminum and likely for gold as well
(although I have never actually looked at this issue with gold). For
precision measurements, you may have to calibrate this effect. If you are
concerned about polarization, that may vary with angle too depending on the
initial state.
--
Adam Norton

Norton Engineered Optics
Optical design and systems engineering for Silicon Valley and beyond.
www.nortonoptics.com

(Remove antispam feature before replying)

Helpful person

Posted: Wed Mar 05, 2008 4:11 am

Joined: 22 Jun 2004 Posts: 692

On Mar 4, 11:00 pm, "Jarvis" <john.jarvis @ yahoo.co.uk> wrote:

Quote:

I'm trying to model the reflectivity of an planar aluminum mirror vs angle..

Basically, I have a nearly monochromatic, 1.5um beam being steered by a
planar aluminum mirror. Angles of incidence vary from about 25 degrees to
65 degrees. I'm seeing some intensity variation as a function of angle of
incidence. (At least I think I am. The apparatus is actually more
convoluted than my simple description and doesn't lend itself to making the
measurement directly.)

I thought it would be "fun" to see if application of the Fresnel equations
to metal reflectors could accurately describe situation. In particular, I
suspect there would be justification for using a different metal reflector
such as gold. I have plenty of signal with aluminum but my measurement
can't tolerate the variation vs angle. This would be an expensive custom
part, so I would like to have some solid justification.

After digging out Hecht's Optics and reviewing what I needed to do, I
realized that the probability of me making a mistake in the calculation is
pretty high. (Additionally, the only complex index data that I can find is
in the Handbook of Chemistry and Physics for 0.8eV (1.55 um). I presume
this data is close enough.)

Am I proceeding along the right path? I was a bit surprised to not see any
aluminum or gold
reflectivity tabulated vs angle at various wavelengths in the open
literature. (Best that I could come up with was normal and 45 degree
incidence in the Melles Griot catalog.) Seems like there should be an
easier way. Is there a reference somewhere that has this data tabulated?
...or do I just need to "grunt it out" ?

Sincerely,

John

If you haven't already, talk with the engineers at Melles Griot and
Edmund Optics. My experience with those at Edmund is that they are
far more helpful than one would expect. (Also, does your aluminum
have a protective overcoat?)

Coater

Posted: Wed Mar 05, 2008 12:48 pm

Guest

"Jarvis" <john.jarvis @ yahoo.co.uk> wrote in message
news:jqqdnbW41LOahlPanZ2dnUVZ_tmhnZ2d@comcast.com...

Quote:

labs. They will be able to tell you what to expect.
But, you must be prepared to answer some questions. Is your current mirror
overcoated? If so, with what, and for what wavelengths?
What polarization are you interested in? S-, P-, Random? Environmental
requirements, temp, humidity, etc. If lasers are used, what power level?
J/cm2, pulse length, rep rate.

But, basically, most front surface aluminized mirrors are overcoated for the
visible region, and for either normal or 45 degree angle of incidence.
1550nm is not usually considered for general run of the mill coatings. Shiny
in the visible region doesn't necessarily mean shiny anywhere else.

And, yes, if you want something to work correctly, you MUST design to your
specifications, and not just buy random off the shelf cheap optics.

Regards,

Coater

whit3rd

Posted: Wed Mar 05, 2008 3:23 pm

Guest

On Mar 4, 8:00 pm, "Jarvis" <john.jarvis @ yahoo.co.uk> wrote:

Quote:

I'm trying to model the reflectivity of an planar aluminum mirror vs angle..

Basically, I have a nearly monochromatic, 1.5um beam being steered by a
planar aluminum mirror.

I think the other responses, that guide you to complex indices
of refraction, are misleading.

Because you probably aren't operating in a vacuum, you do NOT have an
aluminum mirror, you have an Al mirror with Al2O3 overcoat.
The (polarization dependent) Al2O3 reflection interferes with the
underlying
Al reflection.

A table of values won't help, because the oxide layer is unspecified
and changes with time. You might want to model it as a calibration
matter, of course. A gold mirror will only have a minor overcoat of
sticky stuff (like O2 from the atmosphere) and could be more
repeatable (less age-dependent).

Jarvis

Posted: Thu Mar 06, 2008 12:48 pm

Guest

"Jarvis" <john.jarvis @ yahoo.co.uk> wrote in message
news:jqqdnbW41LOahlPanZ2dnUVZ_tmhnZ2d@comcast.com...

Quote:

Thanks all, for your excellent suggestions. I've got enough ideas to keep
me busy for awhile.

FWIW, while poking around, I found the following site,
http://www.ub.es/javaoptics/index-en.html, from Univ. of Barcelona. It
contains a number of java applets to demonstrate optical phenomena. One of
the applets computes reflection coefficients from conductors (although
magnitude of extinction coefficient was limited to too small values to be
useful to me Sad

.

It is worth a look anyway.

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