Magnification: one quick and simple method

As we have seen in my recent posts, knowing the magnification, at say the minimum focus distance (MFD), can be useful, eg for estimating the number of focus brackets we need to take between the MFD and infinity.

Assuming your lens is registered on the PhotonsToPhotos Optical Bench Hub, one can use this resource to get a pretty good idea of lens attributes: at least for a prime lens and where the Optical Bench Hub has a focusing model.

In this post I'll assume the lens you are interested in is not in the optical bench hub, or that you can't focus it on the hub. Also I assume you can’t simply measure the magnification by taking an image of a focused object of known size, at the MFD; for example when using an ultra wide lens with a large depth of field, even at the widest aperture.

In other words, we need to derive magnification experimentally, by estimating the location of the front principal.

Some may be attracted to using a thin lens model, that is magnification (m) is given by f/(u-f), where u is the distance from the front principal, which is also the rear principal in the case of a thin lens, to the object in focus at the MFD.

But we can do better than this by using a thick lens model,  my version looking like this:

From the above it is clear to see why the thin lens model is too simplistic for our needs. But how can we find the location of the front principal, if we don’t know the lens hiatus, ie the position of the rear principal?

There are two lens attributes that can be reasonably well estimated, without complicated equipment: the position of the entrance pupil and the pupil magnification.

The position of the entrance pupil is simply the location of the lens no parallax point, for example as discussed in this post, which can be estimated experimentally, eg using the so-called ‘pole method’ or, say, a laser pointer.

The pupil magnification can be estimated by looking at the lens from the front (entrance) and rear (exit), and either guessing the ratio of the pupil sizes (exit/entrance), or by taking a picture and measuring the ratio.

To illustrate how simple it is, I used my new BrightinStar 9mm, mounted to my Canon R:

By simply rotating the lens on a nodal rail, and using a couple of door posts in the house, I estimated the no parallax point to be about 60mm from the sensor plane. This was a pretty quick estimate and I’m sure I could have been more precise. 

I then put the lens on a light table and took a picture of the lens from the front and back; with a ruler in the frame so I could ensure the same scale when looking at the two images in Photoshop:

From the above we can see the pupil magnification is about 5.

Having estimated the location of the entrance pupil, and the pupil magnification, it is a simple matter to estimate the magnification at the MFD, by simply measuring, the distance from the sensor plane to the nearest object that you can focus on.

In this post I'll make it simpler, by accepting the manufacturer's specification for this distance, ie 200mm, which gives an estimate of the object distance from the front principal of (200-60+9(1-1/5)) = 147.2mm.

Thus magnification at the MFD is 9/(147.2-9) = 0.065

The above also gives us an estimate for where the front principal is located from the sensor, ie at  60 - 9(1-1/5)) = 52.8mm.

So how does ths compare with the marketing blurb?

Well BrightinStar state the lens maximum magnification as 1:13.5, or 0.074.

OK, the two magnifications aren't the same, but they are pretty close; and I’m sure if I had measured the estimated location of the entrance pupil better, I would have got a better magnification estimate.

If I had used the MFD from the sensor (200mm), and the thin lens model for magnification, we would get and estimate of  9/(200-9-9) = 0.049, which is clearly not a good match.

In conclusion, I think the above pragmatic approach is a reasonable one to try, and certainly better than assuming a thin lens model.

As usual I welcome any comments on this post or any of my posts.

Addendum

As mentioned above I thought I’d rushed estimating the entrance pupil location, by using the pole technique, so I redid it and got a distance of 75mm from the image plane. Plugging this into the above equations gives a magnification at the MFD of 0.073. Which is very close to that quoted by the manufacturer, ie 0.074.