In this post I'll be taking a look at the difference between a classic 'View Camera (VC)' or a 'Technical Camera (TC)', ie a VC with additional 'precision' controls, albeit at the loss of a few 'movements'; and a 35mm DSLR with a Tilt/Shift (T/S) lens.
In the post I'll treat the VC and the TC as VCs.
If you are into large format (film) photography, then you are inevitably using a VC. If you are not, and wish to understand a VC, a good (2nd hand book) to look at is Lesile Stroebel's View Camera Technique.
Alternatively, there are many good web sites that help you understand VC or TCs, eg: http://www.mr-alvandi.com/technique/view-camera-focusing.html
The defining feature of a VC is the ability to independently change the position and angle of the film plane and the lens plane, using the so-called Scheimpflug principle(s); as illustrated in this GIF from the alvandi.com web page:
As an historical note, it is worth showing a page from Scheinpflug's original March 1903 patent: No. 751,347. PATENTED FEB. 2, 1904; titled "METHOD OF DISTORTING PLANE IMAGES BY MEANS OF LENSES 0R MIRRORS".
In the above, taken from the 1904 patent, we see in Figure 11 all the information we need to gain insight into a modern tilt/shift lens: something Scheimpflug likely could not have imaged. Note that Scheimpflug's patent includes the important 'hinge line', one focal length from the front principal node, that helps simplify DLSR T/S use, ie the Scheimpflug line is not that much help on its own, we need to know the location of the hinge, around which the tilted depths of field and plane of sharp focus rotate.
Of course in a VC, something that Scheimpflug would have been very familiar with, one can raise and lower the film plane (fixed to the so-called rear standard) and the lens plane (fixed to the so-called front standard) and rotate these in the orthogonal plane, ie swing. For example:
In VCs focus is achieved by moving the front (lens) or the rear (film) standards or both, relative to each other.
As we can see, VCs represent the 'real deal' in photography, giving the photographer full control over all aspects of his or her craft/art.
As this post is more about the 35mm DSLR T/S lenses, I'm not going to discuss any of the details about VCs; other than referencing back to the VC, as a comparison to the DSLR.
Focusing on most modern (non-T/S) DSLRs is achieved via internal focusing, eg where the front lens element(s) and the sensor plane remain fixed, and focus is achieved by moving some of the internal lens elements along the optical axis.
This is a real convenience for most of us, as the lens remains a weather-sealed 'black box', that we don't have to worry about. That is, until, like me, you wish to model the lens, as I have done in DOFIS: see http://photography.grayheron.net/2020/09/dofis-start-of-major-update.html
The DOFIS model, of course, is just that, a model or representation of reality. Only the lens designer knows the 'true' layout of a design and the limitations of the optics and engineering therein.
All I can say is that the DOFIS model, created for Magic Lantern Lua scripting, is a better representation for estimating the depth of fields, especially at less than the hyperfocal and towards the macro end, than the basic thin lens model; ie the one that is in the core ML code.
As a reminder, here is the full DOFIS model:
Of course, for most photographers, most of the time, the difference between using a thin lens model or DOFIS is an irrelevance. The only time where the ML version of the DOFIS model shows any advantage is when you wish to do (controlled) macro photography, or pre-plan some pano photography or undertake focus stacking.
As this post is about T/S lenses, let's now bring in a typical DSLR T/S lens: and see how we can construct a DOFIS version of TiltSim; as, in TiltSim, I only worried about the hinge and distances from the front principal. That is the object space only.
Here is a Canon image of their original 35mm TS-E, showing an 8 degree tilt of the opitcal axis:
As for a representative lens, I can only talk about the lens I have, ie the Canon TS-E 24mm II 3.5L. If I look into the front and the rear of the lens, and move focus and tilt, I can get an impression of what is happening inside, but only an impression.
At the back of the lens I can clearly see the lens optical axis tilting, relative to the back of the lens body, ie that is attached to the camera.
In terms of a VC, the rear standard, ie the sensor plane in my DSLR, remains fixed. That is the image plane doesn't move in space, assuming I'm not tilting the whole camera-lens arrangement (which in this post I won't).
Non tilted, the DoF arrangement (ignoring pupil magnification) looks like this:
Here we see the position of the front principal lens plane, at f*(1+m)+t from the sensor. Where t is the principal plane hiatus.
That is, untilted, a T/S lens is just a normal lens, albeit you paid more for it!
So let's now spend our money and tilt the lens, ignoring in this post how exactly the lens tilts relative to the sensor. As others have published how VCs and tilt lenses work, eg here, I'm not going to duplicate that in this post.
What we see above s just a rework of Scheimpflug's Figure 11, where the DOFIS front principal (H) is the lens plane, the focal plane is set one focal length parallel to the lens plane, the Scheimpflug line (two red dots) is shown, as is the hinge line (green dot). The point of focus and the near and far DoFs, on the optical axis, remain as in the DOFIS model.
Note how the Scheimpflug line is located in two locations, ie separated by the principal plane hiatus: as shown back in 1904.
We also see the Hinge distance (J) = f/sin(tilt). Note that this is measured from the front principal along the tilted optical axis.
DOFIS reports the front principal location, f*(1+m)+t, under additional info. But remember this is along the tilted optical axis.
To see how things appear to work in a DSLR, I've constructed a version of TiltSim, where I've fixed the lens plane and allowed the image side to vary; just to illustrate the relative displacements as we focus:
In the above 24mm, at f/8, simulation, the lens centre is at (0,0) and the sensor plane moves; which in reality it clearly doesn't. The focus in the simulation, along the tilted optical centre, varies from lens minimum to the hyperfocal.
I've tilted the lens by 1.3 degrees, giving a hinge height of just over a meter, also resulting in the optical axis tilting by this amount, ie relative to the orthogonal to the sensor.
A key point to note is that the normal focus distance and DoFs all are calculated along the tilted optical axis, ie not, anymore, the (untilted) axis, orthogonal to the sensor.
BTW I've scaled the image side by 10, as, without doing this, it would be difficult to see the Scheimpflug (sensor) line move, as the movement between the minimum focus distance of the lens and the hyperfocal, is small. Also in this simulation I've ignore the hiatus.
How much movement I hear you say.
As we know, the effective focal length from the sensor is given, assuming a pupil magnification for now of unity, by f*(1+m). That is the lens extension to achieve focus is given by m*f.
At infinity, m is zero, thus, as we know, the effective focal length at infinity is the lens marked focal length: ignoring details of lens design, which may shift this a fraction.
We also know, on my 24mm TS-E, at the minimum focus distance (230mm) the stated magnification is 0.34. Thus the maximum lens extension is 24*0.34, ie just over 8mm of internal movement, ie in the lens focus group of elements. This assumes a simple split/thick lens model.
We also know that at the hyperfocal, by definition, the magnification is (N*C)/f. Thus, with my 24mm TS-E, if I set the aperture to f/10 and use a circle of confusion of 24 microns, the magnification at the hyperfocal is (10*0.024)/24 = 0.01. This also says that at the hyperfocal the lens extension is N*C, ie about 0.24mm in this case.
We also know the hiatus between the principal planes can be estimated from X-(F(1+M)^2)/M, where M is the maximum magnification, ie 0.34, at the minimum focus distance of X, ie 230mm. Giving a hiatus, or value of t, of 103mm. Thus, at minimum focus distance, ie maximum magnification, the front principal, ie the location of J at the lens, is positioned at about 24*(1+0.34)+103mm = 135mm from the sensor: which is about in the middle of the focus band on my 24mm TS-E. A useful thing to know.
So what can we conclude from the above?
First, the hinge line, located at f/sin(tilt), is the piece of information most useful to DSLR TS-E photographers, as once found/fixed, it allows us to position (visualise) the plane of sharp focus and DoFs relative to our lens; and how they rotate as we focus.
Second, the point of focus, ie on the optical axis, and the DoFs, all remain valid if tilting. All we need do is account for the optical axis tilting, relative to the sensor.
Third, because we have a fixed image plane in our DSLR, the hinge plane, ie J position, must move as we focus, ie as we rotate the plane of focus the front principal moves. The height J of the hinge won't change, as this is fixed via f/sin(tilt). Most see this as they try and position the plane of sharp focus, ie a lateral movement of the hinge, along the optical axis, by m*f, ie in my 24mm TS-E, a maximum movement of the just over 8mm. This is why we often have to tweak the tilt and focus a little, ie for perfection ;-)
In future posts I'll talk more about the (yet to be published) DOFIS-based version of TiltSim, ie that accounts for lens breathing, ie focusing, etc: for now, I conclude with my usual sign off.
I welcome all feedback on this post, or other posts on my blog.