collimated reference beams

[Joe Farina]

I was wondering if other holographers have a preferred way to collimate a reference beam.

Some of my holograms lately showed "hotspots" in the middle, which were thought to be from the Gaussian reference beam profile (in DCG maybe a better word would be "hard" spots since the middle of the holograms were clear/narrowband/dim and the outer areas were milky/broadband/bright).

I'm guessing that it may be due to light loss from reflections at different areas of the glass plate, causing outer areas to bounce off more, compared to the middle spot going straight through (which is at Brewster's, 57 degrees, emulsion facing object). With a 60X objective/pinhole, and a 5 X 6 inch plate, I'm guessing that the variation from Brewster's might be as much as 15 degrees at the outer edges. Looking at graphs showing how light is reflected off glass at different angles, I'm thinking that the light loss could be substantial enough to cause non-uniform hardening of DCG.

I would like to try a collimated reference beam to reduce this.

Thanks.

[Din]

You could be right about light loss due to reflections, it depends on the polarisation. Loss of Reflectivity at Brewster's angle only occurs for 'p' (TM) polarisation. Even if you have 'p' polarisation, it would depend on your reference plane. We used a side reference and one problem was to make sure that the plane of incidence was as flat as possible; if the reference beam traveled up- or down-wards, it'd throw the polarisation off. Polarisation is pure 's' or 'p' only if the plane of incidence was flat, otherwise it'd be a mixed polarisation. Another problem could be ratio. You may remember I mentioned how important it was to have roughly a uniform ratio across the plate. If the beam expanded at the edges of your plate, then the ratio at the edges would be lower than at the centre (assuming ratio is defined as ref/obj). Still another factor is the 1/r² fall-off. If the distance from pinhole to edge of the plate varied from the distance to the centre of the plate by a few percent, the edge would get less light.

There are two ways to get a collimated beam - a lens or a mirror. To cover a 5x7 plate, the lens aperture would have to be about 12", and high quality (though this is not as important in display as it is in technical holography). Such lenses are difficult to get and expensive. Another way, used by most holographers, is a collimating mirror. These are mirrors with a spherical profile that take a point source of light - the pinhole - and convert it to a collimated beam, if the pinhole is the focal length away from the mirror. A good source for such mirrors are telescope mirrors from an astronomical supply store. Again, you'd need a mirror with an aperture of about 12", which are easily available. These mirrors are classified by two numbers: the f/# number and the focal length. The f/# number is the ratio of the focal length to the diameter, for example our mirror had a diameter of 12" and a focal length of 36", so f/3.

Important points are:

To be careful as possible to measure the length from pinhole to the centre of the mirror, if this distance is not the focal length, you won't get collimation. A quick-and-dirty method to check for collimation is to allow the collimated beam to fall on a distant area, such as a wall, about 2 or 3 focal lengths away. The beam will be elliptical, but the long side should be the same as the mirror diameter.

Keep the angle between the input beam to the mirror to the output beam from the mirror as small as possible without interfering with other optics. We kept this angle to less than 20 deg. The reason is that these spherical mirrors are designed to be used on-axis, and you'd be using one off-axis. In this case, the output beam is never absolutely collimated, but the smaller the angle, the more collimated it is. At 20 deg it's "good enough for government work" as a friend of mine always says.

[Joe Farina]

Din, thank you for fielding my questions lately, it's been a big help.

In my setup, I didn't use a side reference like you did. My plate was mostly "flat" on the table, that is, one end of the plate was raised/tilted 33 degrees off the table (90 - 57 = 33) and the laser beam (coming in from the other room) was parallel to the table top (and 57 degrees "off normal" in relation to the surface of the tilted glass plate). The polarization should have been correct for the center of the plate, since I checked it by rotating the half-wave plate until the reflection from the glass (on the ceiling) was at its minimum. A good point you made was concerning the "flatness" of the plane of incidence. Last time I checked, the surface of my table was level (using a bubble level) but of course that doesn't mean that my plate (in the plateholder) wasn't twisted slightly the wrong way. I need to look into ways of verifying this. I have an electronic angle finder, which might be useful.

I did a test regarding the uniform light ratio across the plate (nothing to do with polarization, just the Gaussian profile, etc.). My earlier hologram, which had a bad hot spot, had a 26% variation across the plate. I changed this to 1% by moving the plateholder/object further back. This time, the hot spot was substantially less, yet it still remained, which was surprising. So that's why I'm thinking the hot spot was partially due to reflections from angular variations away from Brewster's.

Thanks for the very useful tips regarding collimating mirrors, etc. I should have enough confidence now to try an astronomical spherical mirror.

[holomaker]

Joe, I’m not sure if you mentioned what laser you were using as I read through. But I find the PL 530 laser has a hotspot more so than other lasers do. What that means if you need to throw more light away on the edges and use that central version like you had to with, other typical Diode Lasers , in other words the MFT curve is flat topped (centralized hot spot) ?

[Joe Farina]

Thanks Dave, I'm using a Sapphire 488nm (200mW) right now. The PL 530 is becoming a popular holography laser, it's amazing how much green light is now available to holographers at low cost. By the way, I saw your 275mW green Sapphire head on eBay. I've always wondered to what extent Sapphire controllers can be used (or swapped) for the various Sapphire laser heads. My controller is the OEM version for the 488-200.

[Din]

Joe, I’m not sure if you mentioned what laser you were using as I read through. But I find the PL 530 laser has a hotspot more so than other lasers do. What that means if you need to throw more light away on the edges and use that central version like you had to with, other typical Diode Lasers , in other words the MFT curve is flat topped (centralized hot spot) ?

Do you mean MTF, rather than MFT? The MTF (Modulation Transfer Function) of an optical system is the ability of the system to transfer spatial frequencies, the greater the MTF for high frequencies, the better to resolve sharper edges. But, MTF is not a measure of beam intensity. It's a measure of the integrity of an image when passed through an optical system. If the MTF were flat topped, then it would pass frequencies in a mid-range while having a low- and high-frequency cut-off. Most MTF curves start high in the lower frequency range, while dropping as the frequency range gets higher.

The beam intensity of a laser beam is Gaussian*, unless it has built-in beam flatteners. It's far likelier that the Gaussian is broader at the peak than other lasers. The beam profile of the beam on a white surface may seem far brighter in the centre because the ability of the eye to resolve power is modulated by the photopic function (or the scotopic function in dim light conditions) so it may seem to be of uniform intensity. The only way to tell is to measure the beam along the transverse axis and plot the result. Below is the intensity range of various Gaussian profiles (from "Fundamentals of Photonics, Part 1 - Optics" by Saleh and Teich.) where you can see the look of the beam and the corresponding curves.

*If interested, the intensity of a Gaussian beam is given by:
I(ρ,z) = I₀(W₀/W(z))²exp{-(2ρ²)/W²(z)}
where W₀ is the beam waist, W(z) is the transverse distance and ρ is the beam radius.

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