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Re: [OM] linear polarizers?

Subject: Re: [OM] linear polarizers?
From: Joey Richards <bigjoe@xxxxxxx>
Date: Tue, 18 Jan 2000 12:13:55 -0500
Just a slight correction to your very nice explanation of
polarization and metering:  circularly polarized light is,
in fact, affected by a linear polarizer.  The light that
passes through will be linearly polarized just the same
as unpolarized light would be.

There are two degrees of freedom for polarization, typically
visualized as horizontal and vertical linear polarization.
A vertically polarized light wave has an electric field that
is aligned with the y-axis, a horizontal with the x-axis.
If you have a "diagonally" (linearly) polarized wave, it
would have components along both the x- and y-axes that are in
phase with each other.  A linear polarizer simply blocks one
of these components and transmits the other.

If, instead of in-phase x- and y- components you introduce
a 90 degree phase shift to the electric field along one axis
(eg, the x-component is at a maximum while the y-component
is at a minimum), you get circular polarization.  If the x-axis
is "ahead," you have right-hand polarization (RHP), if it's "behind,"
you have left-handed polarization (LHP) (or maybe it's the other way
around, I am having visualization difficulties this morning).

Note that there are two forms of circular polarization, just as
there are two forms of linear polarization.  Note also that
I described circular polarization in terms of a superposition
of linear polarization states.  I can also describe linear
polarization in terms of circular states -- adding RHP and LHP
waves in-phase results in the y-components cancelling and
you have horizontal linear polarization.  Add them 180 degrees
out of phase and you have vertical polarization.

But, returning to the discussion at hand, circularly polarized
light is actually equally divided along the horizontal and
vertical axes, so 1/2 the amplitude is passed through the
linear polarization of the semi-silvered mirror.  For unpolarized
light (which is to say, randomly polarized light), over any
reasonable time scale, 1/2 of the photons will be passed
through the mirror.  Thus, if the light is circularly polarized,
the _same_ fraction will reach the light sensor as if it were
unpolarized, and the proper exposure will be calculated.


As for using a reversed circular polarizer as an ND filter,
I'm not convinced that it works quite that way.  A quarter-wave
plate does not actually circularly polarize all the light that
passes through it.  Rather, along one linear polarization axis (x),
it introduces a 90 degree phase lag with respect to the
perpendicular axis (y).  If _linearly_polarized_ light polarized
along an axis at a 45 degree angle to the x and y axes enters
the plate, _then_ circularly polarized light comes out (equal
amplitude along x and y with 90 degree phase lag).  If the
light is linearly polarized along x or y, it is lagged, but its
polarization is not changed.  If the light was circularly polarized
to begin with, the output is actually linearly polarized.  In fact,
since every polarization is represented equally in unpolarized
light, the quarter-wave plate has no effect.

And then, on the way out, the still unpolarized light passes through
a linear polarizer, which polarizes it.  I'm pretty sure that a
reversed circular polarizer should be a linear polarizer (I have
neither, so I can't check).

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