How to align a 4F optical system for digital inline holographic microscopy.

The goal of a 4F system in holography is to generate a collimated beam of single-wavelength light, shine it through a sample, and then magnify and refocus this light onto a camera sensor. When the collimated light hits the sample, it creates concentric rings around the objects known as diffraction patterns or Airy discs, like this:

(img credit: fstoppers.com)

These diffraction patterns provide information about the axial depth of the objects in the sample. Using this information we can reconstruct the objects over a 3D volume. This is the basis for holography.

So how do you make a system that will accomplish this task?

Step 1: Focus the L2 lens and camera on a distant object. To do this, you will need to fix your lens and camera to rails. Aim the camera/lens combo at a distant object (like down the hallway). You’ll need a lot of light to make this work, so outside might be best. Then, you’ll need to slide either the lens or the camera in/out until the image you’re seeing is sharp. The focal length of the lens will determine the distance between the lens and camera, so using a ruler to get close will be helpful. Once this is done, affix the lens/camera rail system to its approximate position on the table.

I’m focusing the camera/lens combo onto an illuminated poster about 20 feet away.

Step 2: Use a laser and spatial filter to expand and collimate the beam. This is the hard part until you’ve got some practice. For this step, you’ll need a good collimated laser with a wide beam (3 mm) and enough power to illuminate the sample. A simple laser pointer will not work. An old Melles-Griot laser from the 90s will not work.

You’ll also need a spatial filter consisting of a 10x microscope objective lens and a 25-µm pinhole. Depending on your goals, you may need a different combination of lens and pinhole. These are matched based on the input beam size:

(photo of a Nikon informational poster)

A photo of our spatial filter setup:

(Laser, spatial filter (10x objective & 25-µm pinhole) followed by an aperture to block edges of beam.

To align the spatial filter, you will need to start by getting the laser to shine through the objective lens. I was able to do this by hand, although you may benefit from the use of an adjustable XYZ stage. Once the light shines through the objective, bolt it into place.

Then you’ll need to align the pinhole to the light. The goal here is to start by simply getting the light to shine through. Once you’ve done that, you’ll need to use iterative mini-adjustments to get things perfect. The first time you do this, it can take all day. Stick with it! You may benefit from a light meter at this stage, but it’s not essential.

The most crucial adjustment is the distance from the objective to the pinhole. If set too close, it will produce a bullseye light pattern (this is bad!).

Having the correct distance between the 10x objective and the pinhole is important.

Incorrect distance:

Incorrect distance shows odd patterns and a bullseye appearance

Correct distance:

Correct distance shows a single circle of equal intensity throughout.

Step 4: Position Lens #1 in the right spot. You’ll notice that the beam from the spatial filter is expanding in size. To keep this from happening, add a lens in the L1 position. This position is based on the focal length of the lens. If you need a small system, consider a shorter focal length. Larger focal lengths will give you a bit more margin of error, however. Position the lens such that the outgoing beam diameter remains the same at any distance. I use a piece of paper (sticky notes) with markings to indicate the diameter of the beam. Then I move the paper far away from the lens and check that the diameter hasn’t changed. Once you’ve found the right spot, loosely bolt it down.

Move the L1 lens until the beam is the same diameter at any distance.

Step 5: Ensure the beam is collimated. The spatial filter and L1 lens might be making a nice circular beam, but we need to use a shear interferometer to to ensure it’s fully collimated. The shear plate has two surfaces that reflect the light into two circles like a Venn diagram. When these two circles interact, they “interfere” and create diffraction patterns. The goal here is to get this pattern to run horizontally (parallel to the direction of the light). To do this, you will need to adjust the L1 position and possibly the spatial filter. The gif below shows what happens when the L1 lens is moved towards/away from the spatial filter.

The shear interferometer is essential for positioning L1 and adjusting spatial filter. Note that the angle of the lines change as the L1 lens is moved forward/backwards.

Note that at this step you may find the lines are wavy or impossible to make straight. If this is the case, go back to your spatial filter adjustments and try to align things better. It’s nearly impossible to have it all be perfect, but get as close as you can.

The light will be collimated when the beam stays the same size and the interferometer has nice horizontal parallel straight lines.

Step 5: Add in the objective lens. We’re using a 10x Mitutoyo long working distance lens. Depending on your application, you may want something different. In any case, we position the objective somewhere before the L2 lens that we focused in Step 1. The location of the objective determines, in part, the magnification of the system. Ours is located such that the camera’s field of view is roughly 1 mm across. At this point, you should also bolt down the camera and L2 lens rail system.

Step 6: Insert and focus on a sample. In this system, we focus the sample by moving it forward/backwards in the axial plane. The “microscope” itself does not move at all. The sample should be located between L1 and the microscope objective, roughly at the working distance away from the objective. Here, you will definitely want to use a XYZ stage.

Now you have a 4F digital inline holographic microscope. If done correctly, you will see images that look like this:

A vorticella that has been defocused 1 mm showing Airy discs.

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