# Spatial Filter

As per Newport.

D = Fw/a

D = Pinhole Diameter F = Objective lens focal length w = Wavelength of laser (sorry no Greek letter on my keyboard) a = Beam radius input to lens

#### Positioning a Spatial Filter with a Collimating Mirror

For a collimated reference beam you need to place the spatial filter the sum of the focal lengths of the objective and the mirror apart. The focal length of the mirror is the focal ratio times the diameter.

A great seat of the pants method is to take a piece of poster board and trace the diameter of the mirror on it. Rough set the optics and then place the card so the beam is reflected on to the card from the spatial filter at the largest distance you can find. If it fills the circle drawn on the card then you have a collimated beam. If it is larger you need to move the spatial filter back. If it is smaller you need to move the spatial filter closer. This is all easier and quicker to do without the pinhole.

#### Aligning a Spatial Filter

Aligning a spatial filter is a very difficult task the first time you attempt it. Taking an hour or two is not unusual. After a few tries it is quite easy.

• Remove the Pinhole and the Objective.
• Put a card after the spatial filter, and put a small circle on it around where the beam hits it.
• Replace the Objective, and align the body of the spatial filter so the laser hits the center of the objective, as well as making sure the large disk of light from the objective is centered on the mark on the card.
• Center the X and Y adjustments on the pinhole (so you have as much "room to maneuver" as possible.) and set the Z adjustment so the Pinhole is far away from the objective.
• Re-install the Pinhole, so that the small blob of light (it will be dim) which is making it through the Pinhole hits the circle on the card. (My spatial filter holds the pin hole onto the XY stage with a magnet, its location on the magnet is a course adjustment.)
• Now imagine the hour-glass shape of the light, starting out wide immediately after the objective, narrowing down to the focal point, and then widening out to where the pinhole is. Right now, the pinhole should be approximately centered down stream from the focal point. The adjustment process will walk the Pinhole up the hour-glass till its right on the focal point.
• Move the Pinhole a little bit towards the objective, and watch the blob on the card. If the blob stays centered as you get closer to the objective, keep adjusting it closer to the objective. If it moves off center, stop and tweak the X and Y adjustments to re-center the blob.
• Note how the blob moves in the same direction as the X and Y adjustments. If you go too far towards the objective and pass the focal point, the X and Y adjustments will reverse direction.
• Keep moving the Pinhole towards the Objective, recentering the blob as you go. As you get closer, the adjustments will get touchier and touchier. If you lose the blob, move the Pinhole away from the objective till it re-appears, re-center, and then continue from there.
• At some point, as you get closer to the focal point, rings will become visible around the blob of light. Those are Arie rings from the laser diffracting off the edge of the Pin-hole, and a good sign.
• Keep moving the pinhole closer (and tweeking the X and Y to keep the blob centered) until the Arie rings merge with the blob. The blob will start getting brighter very quickly as you get close.
• When the Arie rings merge with the blob, you're done.
• If the X and Y adjustments reverse directions you've over-shot, the Pinhole is between the focal point and the Objective. Move the Pinhole away from the Objective, and then continue from there, just like if you lose the blob.

The adjustments will be large as you start, perhaps an entire turn of a thumb screw. As you get closer to the focal point, a 5 degree rotation may overshoot.

#### Homebuilt Spatial Filters

When building home made spatial filters it is good to consider the very fine threads from [Thor Labs]. They have taps and pre-made inserts. The pre-made inserts are much easier to use. The 100 TPI screws only have a thread height of .006" and it is hard to drill a hole that smooth. If you need to the proper method is to drill the hole under-size and ream it to size with a straight reamer.

#### Color Holography

The assumption is that you have combined the beams into a single path and you have telescopes on the beams before the beam combiners so you can control their diameters. (The further assumption that the divergence of the lasers is the same.) As we will see you don't want all of the beams to be the same diameter!

Quote: From Edmund:

1.0 Beam Spot Diameter (microns) = (1.27 * l * f) / D

where, l = wavelength of laser (microns) f = focal length of objective lens (mm) D = input beam diameter (mm)

2.0 Pinhole size is then determined for the table (see note): Pinhole Diameter (microns) = 1.5 * Beam Spot Size Diameter (microns)

So we notice that wavelength makes a difference.

For this example we will use the wavelengths of:

650nm 532nm 473nm

In order to make white we need the beam spot diameters of all three beams to be equal. If we miss, the balance of white will be uneven radially from the center out.

dspot=(1.27*.650*f)/D dspot=(1.27*.532*f)/D dspot=(1.27*.473*f)/D

We will choose 8mm as the focal length of our objective in the spatial filter.

dspot=(1.27*.650*8)/D dspot=(1.27*.532*8)/D dspot=(1.27*.473*8)/D

dspot=6.604/D dspot=5.405/D dspot=4.806/D

In order to allow more light through we multiply a correction factor of 1.5 to the calculated values.

Pinhole=9.906/D Pinhole=8.108/D Pinhole=7.209/D

Now we are using only one pinhole and we need three beam diameters to make three equal spot sizes.

If our red laser is 10mm then we use a 10 micron pinhole. For green the beam needs to be 8.1 mm in diameter. The blue beam needs to be 7.2 mm.

Now the last equation we need is a way to change the diameter of our laser beams.

In order to make a beam larger (or smaller really) we need to understand a very simple equation.

InputD/OutputD=fl1/fl2 when the lenses are at fl1+fl2 distance apart.

So if our red laser is 10mm dia. And our Green laser is 5mm then we need a telescope in the path of the green laser in the ratio of 5 to 8. If the lenses we have access to are 50mm and 80mm focal length then we place them 130mm apart and in the path of the green beam before the beam combiner. Now for example if the blue laser is 2.5mm we need to be 2.5 to 7.2 ratio and we could choose 25mm and 75mm focal length lenses placed 100mm apart. Now when we combine the beam we get a true Gaussian white beam. When we pass them through the spatial filter we have a white Gaussian spot with no color variation across the beam diameter.

Note these same equations can be used to Circularize an Elliptical Laser Beam using cylindrical lenses.

For reference: