Poor Man’s Optical Bench

There are two types of photographer: those that like/need to understand their lens and its characteristics; and those that treat the camera+lens as a simple system, with the sensor as the zero or reference point. 

For a lot of photography, for example single image landscape capture, where objects are greater than, say, half the hyperfocal distance or more, treating the sensor plane as your reference point is not unreasonable.

However, for macro photography, pano photography, or, say, deep focus landscape photography, when you need to focus bracket from or near the minimum focus distance, knowing a few things about your lens is helpful/necessary. For example: 

• The location of the entrance pupil, which is the no parallax point of a lens when taking panos. It is also the location from where the hyperfocal distance is measured
• Position of the front principal, from where depths of field are estimated
• Focal length at non infinity focus, that is lens focal length can/will change during focusing, especially when using a macro lens
• Pupil magnification, which becomes important when carrying out macro photography

There is only one source of lens information that is ‘right’, namely that which the manufacturer holds, but that is not knowable by the lens user. 

The next best source of information/insight is provided by PhotonsToPhotos Optical Bench. 

However, even the PTPOB doesn’t cover all situations, for example, not all primes have the ability to be focused in the hub; and none of the zoom lenses have a focusing feature. Plus, not all lenses are listed. Having said that, the PTPOB, is an incredible resource and the photography community should be thankful that Bill Claff maintains the resource as freely accessible. 

As many photographers know, one can get some insight into a lens by using the so-called thin lens model:

Its attractiveness to many is its simplicity, and, for non macro work, it helps photographers begin to understand their lenses, eg in terms of the lens focal length and magnification. However, the thin lens model places pupils and principals at a single location, and breaks down as you approach the macro regime. It’s also not helpful for the pano photographer.  

For this reason, many, like myself, prefer to use the so-called thick lens model, that accounts for lens pupils and principals, where they cross the axis of the lens:

 

As can be seen, the thick lens model allows us to identify all the important characteristics of a lens at a given focus, identifying the focal points, the front and rear principals, and the entrance and exit pupils. 

 

 

In order to speed up using the thick lens model, I’ve written a graphical calculator that is useable by all. I’ve written the calculator in the Desmos environment, and called the calculator, The Poor Man’s Optical Bench (PMOB), in homage to the PTPOB. 

You can access the PMOB by clicking on its link on the RHS of this page or this link. You don’t need an account and only need to enter a name of some kind. 

The calculator has two pages with page one showing some information on the calculator and where you type in the lens name, or leave the text field at the bottom of the page blank. 

 

Moving to page two we see two areas. On the left is where you put your input data, ie:

• Focal length, as printed on the lens, or estimated or reported on a zoom
• The f-number at infinity, ie as set by your camera or set on a manual lens. This is used when estimating the hyperfocal and the number of focus brackets from the minimum focus distance to infinity
• The minimum focus distance, measured or taken from the manufacturer’s data; as measured from the sensor plane
• The pupil magnification

• The entrance pupil location, ie the no parallax point
  
• The focus distance, as measured from the sensor plane
• The sensor size, which is used to estimate the field of view or acceptance. Use 36, 24 or 43.3mm on a full frame camera, ie width, height or diagonal
• The circle of confusion in microns
• The final input field is used to change the line spacing on the output text, which is useful as you zoom in and out of the calculator's image
  

For a prime lens the infinity focal length and infinity f-number are those printed on the lens or as reported by the camera or on the lens for a zoom. The pupil magnification, exit pupil diameter divided by the entrance pupil diameter, measured or estimated, needs to be entered (see here). With the lens mounted on the camera, and on a nodal rail, one can use the pano no parallax method, or a laser leveller with the lens on a table, to estimate the location of the entrance pupil (see here).

The graphic on the right of the page then will provide you a visual of the lens field of view, and the layout of the pupils and principals on the axis. it will also tabulate the inputs and some calculated outputs, that can be used to refine the model, ie to ensure magnication matches. A printed out screen grab of this page will serve as a reference sheet.

In the above we see the end result of the following workflow:

1. Capture and enter all the input information, ie measured or taken from the manufacturers lens specifications or the PTPOB.
2. Once entered, check that the magnification is as expected or measured. If not adjust the focal length until the magnification is as expected.

In the above example, for a Canon 100mm macro lens, where, for convenience, I took the entrance pupil location from the PTPOB, we see that at a magnification of unity, ie at the minimum focus distance, the focal length is in fact (around) 74mm, ie where the calculator's magnification becomes unity, this focal length compares well with the PTPOB.

 

The calculator also provides an estimate of the maximum number of focus brackets needed to go from the MFD to infinity. The hyperfocal distance from the sensor is also estimated.

One final thing to note is that the PMOB is a spot model, meaning that it is only suitable for assessing a lens at a single point of focus. The model doesn’t allow you to explore focusing, as it doesn’t model how the principals and pupils change during focusing.

 

Also the Poor Man's Optical Bench is no replacement for the PTPOB, nor will it ever. It is also based on the accuracy of estimating the location of the entrance pupil, the pupil magnification and the optical magnification.

 

As this has been a long post, I'll stop here, as my intention in this post was to introduce the calculator. I'll be writing other posts illustrating the calculator’s potential value to photographers.

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