Wollaston Landscape Lens

Introduction

The Wollaston Landscape Lens has the distinction of being a photographic lens invented before photography. It was originally conceived by William Hyde Wollaston in 1812 for the camera obscura, but was later adopted by early photographers. It consists of a single meniscus lens and an aperture stop between the lens and the object. Today cameras lenses are designed with considerably more optical elements and the aperture is buried inside. Also unconventionally, the meniscus lens is mounted with the concave side toward the object. Modern camera lenses have the familiar bulge of the convex surface of the first lens visible.

Analysis

Lets start with the basics. The most common lens is the double convex and it focuses light pretty well all by itself. Due to something called spherical aberration, the rays don't meet exactly at the point on the right. Rays that hit the lens further from the axis focus slightly closer than those in the center. It isn't that noticeable in the middle of the image, but as we will see, it gets worse the further out you go.

Now a positive meniscus lens does about the same thing, but it's spherical aberration is so bad you can actually see that the rays are not meeting at the same point even in the middle of the image. About now you might be wondering why anyone would even think of trying to use this lens to make an image, but stay with me.

When light rays are coming from the side, you can see that the double convex lens is still doing an okay job of focusing the light to a point. The lens creates a image, but on a curved surface. That means that when the image is projected on a flat surface, like a piece of film, it will be in focus in the middle, but will be less focused the further you get from the center. This is called coma aberration.

The meniscus lens does a terrible job of focusing. The rays are all over the place as it tries to focus light from off the axis. However, notice that the two bottom rays going through the lens are actually focusing where they should on the right!

Now we put an aperture stop in front of the lens so it limits the light passing through the lens to just this "sweet spot" where it is bent just right to hit the image plane. This is the magic of the Wollaston Landscape Lens.

If the stop is too close to the lens, it doesn't work as well. You can probably see that the rays are focusing a little early and we have a curved image again.

And if the stop is way too far from the lens, the rays miss the lens entirely due to its limited diameter. So the stop has a position where it helps to flatten the image field but doesn't get in the way.

We can try moving the stop position while sweeping out the image surface. In the first trace you can see that if the stop is against the lens you get the very curved image we have been talking about. Moving the stop further away keeps flatting the field more, but at about 18mm the flatting is as good as it gets. Then the image starts to curve more again, and just a little further away is where the diameter of the lens becomes the limit.

Comparing a Double Convex to the Wollaston

Above we saw how nearly perfect we can make the focal plane with stop position. Now lets compare a simple Double Convex DCX lens to the Wollaston Landscape. Below is the very curved focal surface for a DCX lens. It is bound to have trouble focusing when you get off axis.

Two photos below were shot with the same 4x5 camera at f32 on to enlarging paper. The one on the left is the DCX and the right is the Wollaston. At first glance they look pretty similar especially at this print size. There is a little vignetting in the Wollaston because the lens is too small for a 4x5 image.

The middle of the DCX image is actually better than the Wollaston due to the lower spherical aberration of the DCX lens over the meniscus.

But look off to the side and you can see how degraded the DCX image is compared to the Wollaston. These images come from the left end of the white fence.

How far should my stop be?

At the risk of stating the obvious, it depends on your specific lens design. There are an infinite number of curvature pairs that will create a lens with the same focal length. The concave shape of the first surface is critical to the geometric ray selection process. It turns out that the more "bent" the meniscus lens is, that is the more curved both surfaces are, the closer the stop will end up to the lens.

There is a lens design parameter called the Coddington Shape Factor that quantifies the bend. I've drawn some lens cross-sections with equal focal length but variations in the shape factor. The -9 is the absolute extreme case of a sphere on the right surface and the -1 is a plano-convex (PCX) lens with a flat left side. The stop distance is inversely related to this shape factor. Unfortunately, when buying surplus lenses, you only get the diameter and focal length. My guess is the bulk of small meniscus lenses you are likely to run across have a shape factor around -2.

Stop Distance = (n-1)/n x fl/sf

Where n is the index of refraction of the lens, fl is the focal length, and sf is the shape factor. Using 1.52 for the index; that becomes:

Stop Distance = 0.34 x fl/sf

and a shape factor of -2 for a rule of thumb:

STOP DISTANCE = 0.17 x fl

or about 1/6th the focal length.

What about the Plano Convex ?

For the Plano Convex PCX, the equation simplifies to Stop Distance = 0.34 x fl for glass. That probably puts the stop impractically far forward. The diameter of the lens would need to be very large to allow off axis light to even hit it. It is important to use the lens shape factor to shorten the distance. As much as I appreciate Alan Greene's book " Primitive Photography," unfortunately his Wollaston design uses a PCX not a meniscus. I'm pretty sure he just puts the stop as far forward as possible to not vignette his 8 x 10 image frame, but no where near where it needs to be to flatten the image field. The problem is that surplus meniscus lenses larger than about 35mm in diameter tend to be really PCX as the concave side is just too shallow for a Wollaston. By the way, the Double Convex DCX is symmetrical and has a shape factor of 0. The distance equation goes to infinity telling you there isn't anyway to position a stop to fix the field curvature.

Where does this equation come from?

The ultimate goal is to arrange for the lens to focus to the same distance no matter what angle the light comes from. In other words, flatten the image field, and if the image field is flat, just about everything else will take care of itself. The PCX might be the least practical way to make a landscape lens, but it is the easiest place to see what is going on because the right lens surface (radius R2) does most of the work.

In the figure below I've reduced all the rays to only two leaving the stop and striking the lens near its edge. I haven't drawn rays along the axis, but it should be easy to imagine that two rays symmetrically above and below the axis would hit the right lens surface nearly perpendicular and focus on the axis somewhere to the right. However, other pairs not striking the right surface in the same way will end up not symmetrically bent and will always focus closer. So we put a stop at a distance so that the parallel rays are first bent by the plano surface to become nearly perpendicular with the right surface again. That way they are focused as far as possible to the right and thereby potentially flattening the field. That distance is simply the radius of the right surface divided by the index of refraction of the lens or R2/n.

R2 in the example above is 26mm which means the lens is focusing at 50mm. The stop is at 17mm but notice that is measured from the right lens surface NOT the edge. The lens is 3.5mm thick so the stop is physically 13.5mm to the left of the lens edge. The lens must be 26mm in diameter to catch the rays that are at 40 degrees. Everything scales with focal length, so a 100mm focal length version would have a R2=52mm and the stop distance of 34mm and a lens diameter of 42mm.

Now lets add a negative curve to the left surface. The shape factor is now -3 and the diagram below shows the result. You can't tell, but the focal length has doubled to 100mm. The surprising thing is that the same position of the stop is creating nearly the same effect as before. So we doubled the focal length but left the stop distance and lens diameter the same. The stop distance primarily depends on R2 and the index!

Getting back to my Stop Distance = (n-1)/n x fl/sf equation. Although R2 is really the ideal value to use, I thought you would more likely have the focal length, could probably guess shape factor and assume the index of refraction. That way R2 could be computed from these known values. However, if you go through all the algebra, you still won't get exactly my equation. I also ran many examples and tried to account for the lens thickness to make the measurement from the lens left edge and not the right surface as the R2/n equation does.

Working from R2

A couple things are effecting the way a lens works besides the curvatures. The two drawings below show the same focal length lens (100mm) with the same shape factor (-3) but with different diameters on the left and different edge thickness on the right. Both diameter and edge thickness change the total thickness of the lens which naturally changes the way it refracts light. Especially when you consider we are using different parts of the lens depending on where the light is coming from.

Referring to the diagram below. You need to very accurately measure the total thickness t, diameter d, and edge thickness e with calipers. Plug the numbers into the equations below and get the stop distance.

b=t-e

R2=(4b^2 + d^2)/(8b) where b^2 means b squared

Stop Distance = (R2 - t)/n measured from the left edge and assume n=1.52

All that said

You need to consider something maybe not so obvious. What is the focal length of a meniscus lens? If you look back at the ray tracing for the on axis meniscus, the spherical aberration is so bad it is really a range of focus. The larger the diameter of the lens, the wider the range so that is why you seldom use a stop larger than f/11 for a Wollaston. Also, the objective of making the image field flat is as arbitrary as any other goal you might have. It is unlikely that a both simple and accurate equation is going to capture all the optical interactions in even this simple system. The good news is that the optimum stop distance is not sharply defined. Plus or minus 20% won't make a significant difference in the image. At the very least, these equations will get you close.

Wollaston's Original Design

I happened across some pages from a 1920 French optics book by Turrière called "Optique industrielle" posted on an Italian website. It is a little hard to figure out, but it looks like Wollaston's original camera obscura lens prescription is given along with a 100mm focal length redesign. The original design focal length was 560mm or 22 inches which would be obviously too long for photography. Taking the given lens surface radius, the lens had a shape factor of exactly -3 and the aperture was located at -70mm. Fortunately, Wollaston's original 1812 paper to the Royal Society is available here. In it he doesn't give values, but does state that the ratio of the curvatures should be 2 to 1 and that would be a shape factor of -3. His lens was 4 inches in diameter and a 2 inch diameter stop for f/11. He also says the stop should be at 1/8 the focal length. That is -560/8 or -70mm agreeing with Turrière . My equations would put the stop at around -90mm, but that would greatly limit the field of view to completely flatten the field. Wollaston understood how the distance scaled with focal length, but probably didn't realize exactly how this distance was effected by the shape factor. By the way there is an excellent biography, "Pure Intelligence: The Life of William Hyde Wollaston" by Melvyn C. Usselman that was published in 2015.

Chromatic Aberration

So far the analysis has been with only one color of light. Unfortunately glass doesn't treat light the same for all colors. It bends blue more than red and green is between. If we focus white light on axis, you can see what is happening in the highly magnified area where the spot is focused. Blue is too early, red is too late and green just right. However, the entire spot is only 0.06mm in diameter and for an image 60mm in diameter. That is about 1 Megapixel resolution!

But what is happening out at the edge of the image? Again looking at the area at the image plane where the spot should be, you can see that the blue is still focusing early. Green is right on the plane and red a little beyond, but the spot is much bigger at 0.3mm diameter. Not exactly high resolution, but consider a pinhole camera with optimum hole size would would be about 0.4mm blur. So it is doing better than a pinhole at the far edges of the image and six stops brighter to boot.

When the Wollaston Landscape lens was adopted for photography, Charles Chevalier used two lenses, the achromatic, to help fix the color aberration problem. Initially his design used a plane surface acromatic but later adopted the familiar meniscus shape to shorten the stop to lens distance. This became known as the French Landscape lens.

In his book "A History of the Photographic Lens," Rudolf Kingslake says:

Actually the lack of correction of both chromatic and spherical aberration has the effect of increasing the depth of field of a simple box camera. The image of an object located at some particular distance from the lens is in focus for certain combinations of lens zone and wavelength of the light, while it is more or less out of focus for other zones and wavelengths. The picture formed on the film, therefore, consists of a sharp image superposed on a slightly blurred image, but as the sharp image is likely to be brighter than the blurred image, it will be more strongly imaged on the film, particularly if the exposure is on the lean side. Over exposure will, of course, record everything, resulting in a somewhat blurred and "mushy" negative.

The Kodak Company fitted acromatic lenses to their better cameras for many years, and they also made some semiachromats in which the cemented interface was plane, but they finally abandoned achromatic landscape lenses after they found that the average user could not detect the difference.

Kodak Brownie

I thought I'd go through the most famous example of a box camera with a Wollaston Landscape lens. The original Kodak Brownie Camera. Here is the patent drawing with the image (28) plane on the left and lens (6) on the right. Scaling the drawing from known film dimensions, I think the lens was about 15mm diameter and 100mm focal length. I know this isn't a technical drawing, but looking at the lens shape in cross-section, it looks to have a shape factor of about -4. The space from the lens to the stop looks like about 8.5mm.

Given the assumed lens design and spacing, here is the image surface for the Brownie. Not too bad and certainly better than what they would have gotten with a simple double convex lens.

I managed to buy a couple Brownies on Ebay the other day. I thought the smaller one might be one of the original versions, but it turned out to be a later special simplified model that was given away to 12 year old children to celebrate Kodak's 50th anniversary in 1930. Basically it only has one stop at f/16 and one shutter speed at 1/50s. Truly point and shoot for a sunny day. It also has a 2 1/4 x 3 1/4 format and a 108mm focal length 14mm diameter lens. By focusing a reflection of the sun off of the concave surface of the lens I estimated its curvature., and with that I can calculate the rest of the prescription. Turns out this lens has a shape factor of -2.8. Plugging into the equation it says the stop should be at 18mm. It actually measures closer to 12mm, but it is little hard to make really accurate measurements.

Several Examples

Here are example shots taken with three Wollaston designs at f/32 1/4s and a pinhole at f/270 30s onto 4x5" format using enlarging paper for film:

1. 50th Brownie - Lens taken from the 50th Anniversary camera lens described above, shape -2.8 and stop @ 12mm

2. Surplus - Surplus Shed 21x103mm (L7402) positive meniscus, shape -3.6 and stop @ 10mm

3. Compound - Made by mounting plane sides, a 37.5x-90.5mm (77-040) Plano Concave to a 42x48.5mm (77-882) Plano Convex from Edmund Optics, final shape -4 and stop @ 11mm

4. Pinhole - 0.015" hole at 4"

The Brownie and Surplus designs are nearly identical with similar vignetting . The Composite really shouldn't have vignetting, but unfortunately my simple homemade camera body wasn't quite able to accommodate the longer focal length of the combined elements. Finally the Pinhole shows just how capable they can be, but at an exposure over 100 times longer.

In the center of the image the Brownie and Surplus are very similar. The Compound shows noticeably better resolution. Notice especially the contrast of the tree branches. The Pinhole is somewhat washed out compared to the lens photographs.

Getting off center, again the Brownie and Surplus are similar, but the vignetting of the Brownie is more noticeable. The Compound it clearly the best. As expected, the Pinhole is holding its own compared to the Brownie and Surplus as we get off axis.

A Big Brownie

Another of my Brownie camera finds is the No.2-C Model A. It has a big postcard size image of 2 7/8" x 4 7/8". More interestingly, it uses an achromatic meniscus lens. Actually Kingslake called it a semiachromat since it was a plano-convex cemented to a plano-concave. The lens can be removed by unscrewing a retaining ring from the inside. Even though the camera isn't destroyed by the process, there is little chance of ever running film through it anyway. You can just make out the two cemented lenses in the image below. The combined lens shape factor is -3.4, 24mm diameter and a focal length of 144mm.

I remounted the lens into a PVC tube that fits my 4x5 pinhole camera, and made up stops for f/22, 32 and 45 that just press into the tube end. My camera uses a simple shutter that is a vane rotated away from the lens with a model airplane servo for a timed period. The controller is in the white box on the top with a knob to adjust the time. For pinhole use, it is normally rotated and left for possibly minutes. For the Wollaston lens it only rotates for 1/4s.

Here are some example photos taken with the lens shot onto multigrade enlarging paper. I used a Yellow Y2 or Wratten #8 type filter for the one on the right. I've now experimented with six different Wollaston designs. and this is the best so far, and only cost about $10 for the old Brownie camera on eBay.

One Last Thing

Apparently, you can buy a new Wollaston Landscape Lens for large format photography. I really don't know much about this lens, but if you are interested here is the link.