The optics of circular polarizers in photography

[Redbelly98]

For some years I've had a nagging question about the details of how a circular polarizer, as used by photographers, actually works. After a google search, I see lots of sites saying that the filter consists of a linear polarizer and a quarter wave plate. The wave plate is supposed to "circularize" the incident linearly polarized light. This is desirable because the optics in an SLR camera (in particular, the partially transmitting mirror) are designed to have equal amounts of the two linear polarization components. Both randomly and circularly polarized light will work; linearly polarized light will not.

Okay, here is my problem: wave plates are designed to work at specific, discrete wavelengths. But visible light is comprised of a continuous spectrum, covering nearly a factor of two range of wavelengths (400 to 700 nm). So if a specific wavelength in that range gets circularly polarized, other wavelengths will not be; the "quarter wave" plate will be the wrong thickness, and give the wrong amount of relative phase shift, for most wavelengths in the visible range.

I have thought of two possible ways in which these filters could work:

1. the wave plate produces a λ/4 relative shift at about 550 nm, in the center of the visible spectrum. Light of other wavelengths are elliptically polarized, but it still works well enough for the purpose at hand.

2. the wave plate produces a relative shift of nλ, where n is a large number (not necessarily an integer) for visible wavelengths. For some wavelengths, n will be an integer ±¼ and the light is truly circularly polarized. But in general different wavelengths are polarized elliptically. The mix of the two linear polarizations is pretty equal, on average, so this does not present a problem.​

Does anybody know which of these cases correctly describes circular polarizers? Or is something else going on?

 

[Cthugha]

Okay, here is my problem: wave plates are designed to work at specific, discrete wavelengths. But visible light is comprised of a continuous spectrum, covering nearly a factor of two range of wavelengths (400 to 700 nm). So if a specific wavelength in that range gets circularly polarized, other wavelengths will not be; the "quarter wave" plate will be the wrong thickness, and give the wrong amount of relative phase shift, for most wavelengths in the visible range.

I do not know whether this approach is too expensive for usage in photography, but you can use achromatic waveplates that have a rather shallow dispersion over a rather broad wavelength range (200-400 nm broad). Here you use two waveplates made from different materials which offer opposite dispersions and can thereby compensate for the dispersion partially.

For example Thor Labs have a comparison of "common" and achromatic waveplates on their page:

http://www.thorlabs.de/images/TabImages/AHWP05M_Chart_1200px.jpg"

 

[NobodySpecial]

Okay, here is my problem: wave plates are designed to work at specific, discrete wavelengths.

These aren't 1/4lambda thick plates they are a thin birefringent material (with different refractive index in each polarization) the 1/4 wave should really be thought of as 90deg phase - it's not a thickness.

The birefringent material aren't that dispersive the 90deg phase difference is pretty much constant over the visible band.

 

[dlgoff]

These aren't 1/4lambda thick plates they are a thin birefringent material (with different refractive index in each polarization) the 1/4 wave should really be thought of as 90deg phase - it's not a thickness.

Looking at my optics text, it explains that the thickness, d, is chosen to make the difference n1d - n2d equal to 1/4 wavelength. Where n1 and n2 are the indexes. Just saying.

 

[Redbelly98]

I do not know whether this approach is too expensive for usage in photography, but you can use achromatic waveplates that have a rather shallow dispersion over a rather broad wavelength range (200-400 nm broad). Here you use two waveplates made from different materials which offer opposite dispersions and can thereby compensate for the dispersion partially.

For example Thor Labs have a comparison of "common" and achromatic waveplates on their page:

http://www.thorlabs.de/images/TabImages/AHWP05M_Chart_1200px.jpg"

Hey, thanks! Hmmm, the $780 price of http://www.thorlabs.com/NewGroupPage9.cfm?ObjectGroup_ID=854" is a lot more than the $50-or-so price of a photographic circular polarizer. Makes me wonder if that is what is going on with the camera filters. Relaxing some of the specifications, like damage threshold and surface quality, would bring the price down, but we are talking an order of magnitude on the price here. Still, it may be possible to do what you suggest cheaply enough.

These aren't 1/4lambda thick plates they are a thin birefringent material (with different refractive index in each polarization) the 1/4 wave should really be thought of as 90deg phase - it's not a thickness.

The birefringent material aren't that dispersive the 90deg phase difference is pretty much constant over the visible band.

Hi,
I'm aware of how wave plates work. Waves of the two orthogonal linear polarizations travel at different speeds through the material. To the extent those speeds are independent of wavelength, the two polarizations become offset by a fixed amount of time for a fixed plate thickness. This time difference will correspond to 90°, or a quarter of a cycle, only for certain wavelengths. It is not 90° for all wavelengths.

In other words, you get the red curves in these plots:

http://www.thorlabs.com/images/TabImages/AQWP05M_Chart_1200px.jpg

Note how the retardance varies from 0.22 to 0.42 waves, or 80° to 150° in phase, over the visible range of 400-700 nm.

 

[Andy Resnick]

For some years I've had a nagging question about the details of how a circular polarizer, as used by photographers, actually works.

Good question- Tiffen and Hoya both manke good ones, and neither gives details about the components. The only achromatic retarders I know of are rather thick, but these guys:

http://www.optigrafix.com/circular_polarizer.htm

make a thin film retarder.

 

[NobodySpecial]

Remember the photography ones don't have to circularize all colors equally - they just have to put enough of the polarized light back into circular for the AF to work - it doesn't have any effect on the photo.

 

[Redbelly98]

. . . these guys:

http://www.optigrafix.com/circular_polarizer.htm

make a thin film retarder.

The exit beam's longitudinal polarization, between the wave plate and polarizer, is rather interesting...

 

[K^2]

If you hit the quarter-wave plate at 45° with light that isn't at the right frequency, what you get is elliptically polarized light instead. If you place a quarter-wave plate that's designed for 500nm, deep red and deep blue will be slightly elliptical, but for purposes of photography, it's going to be pretty much the same thing. You won't notice a 10% difference in intensities between the two axis.

 

[Andy Resnick]

The exit beam's longitudinal polarization, between the wave plate and polarizer, is rather interesting...

Heh... I'm thinking that's just the way they drew it.

Although in the near-field, there is a longitudinal polarization component.