Ball Lens Microscope Optics

Introduction

Antonie van Leeuwenhoek didn't invent the ball lens microscope

Ball Lens Basics

A ball lens is just a sphere of transparent material. Most transparent materials, like glass, have an index of refraction that causes light entering a ball lens to be focused just outside the opposite side. Because of the relatively high curvature of the surfaces, the focal length of a ball lens is very short. The figure below illustrates how two parallel rays of light are bent to a focus just to the right of the lens.

Unfortunately, the light focusing effect is imperfect. The further from the optical axis the light enters the ball, the closer it is focused. This is called spherical aberration and is illustrated below. This spread in focus leads to a blurry image.

In a ball lens microscope, the light is direction is actually reversed from what I've shown. It is coming from points on a specimen and should be made parallel by the ball lens. These parallel rays will be focused by another lens, either in your eye or a camera, back to a point on an image. However, the spherical aberration causes the more distant rays to not be parallel as shown below.

Since the outer rays are bent lightly inward, they focus too early in the eye or camera. This also leads to a blurry image. The illustration below shows the point on the specimen poorly focusing on the far right. The lens in the middle is either the one in your eye or camera and the image plane on the right is either your retina or light sensor.

The simplest way to fix the spherical aberration is to limit the rays to only ones close to the optical axis. This is accomplished with a small circular aperture between the ball lens and the rest of the optical system. Now the focus is to a point, but at a loss of the brightness.

Some of the light coming off the specimen will enter the lens and exit the aperture, but never enter the eye or camera. Generally these oblique rays cause a loss in image contrast because they are scattered by imperfections in the glass or are randomly reflected in a way to create an overall image fog.

So, the contrast can be improved by putting a second aperture between the specimen and the lens that prevents light that would never reach the image from ever getting into the system. This aperture can be about twice as large as the one on the image side without causing any reduced brightness or field of view.

We now have the complete ball lens microscope optics; A specimen side aperture, ball lens, and image side aperture.

Before going on with the analysis, is is worth noting a few optical things. First, a large part of the ball lens is not doing anything at all. As illustrated below, the ball could be reduced to a cylinder since no light is traveling in the outer areas.

Also, it is the surface of the glass that is doing the bulk of the work in changing the light rays. The body of the glass could be eliminated and we would still have a similar lens. With only a slight tweek in curvature, the lens below has the same effect as the full ball lens shown before. In fact, Antonie van Leeuwenhoek preferred to use this type of lens over the ball.

Sizing the Ball and Apertures

I won't go into where the equations come from.

Making a Ball Lens

Testing the Lens

Below I've imaged a small double convex lens that I purchased from Surplus Shed. It was probably intended for the eyepiece of some optical equipment, but it has about a 4mm focal length similar to the ball lens we are trying to make. Notice how the spherical aberration distorts the grid, but in the center the grid is essentially square.

The most common problem with flame worked lenses is that they end up slightly Q-Tip shaped. This results in an asymmetrical magnification of the grid and in the center you can see that it is no longer an exactly square image.

With practice, a flame worked ball can be made symmetrical (at least in the middle). The center of the image can be as every bit as good as the traditionally ground double convex lens.

Making the Microscope

Using the Microscope

The images below were captured by simply holding the microscope up to the camera in my phone. They really don't look as good as what you actually see with your eye, but they give you an idea of what you can see with a ball lens microscope.