Talk:Scheimpflug principle

Scheimpflug
This article is screaming for some additional figures. Fig. 1 is awesome, pulls you right in. Where is the same picture showing in focus achieved by lens tilt? Where is the same picture showing focus achieved by backplane tilt (perspective loss)? Demonstration of the Scheimpflug solution would add tremendously to the impact of this article.

Note: a single object must be for all three example images to consummate the paper. Changing objects detracts from the message. — Preceding unsigned comment added by 59.27.183.94 (talk) 20:33, 29 July 2013 (UTC)

Refinement/addition to the Scheimpflug principle
This mat'l is rather arcane to add directly, but whoever edits it into shape needs to understand....

The image created by a lens is inverted vertically, horizontally, and also in distance from the lens -- depth. We recognize the 2-D inversion, which is directly proportional - objects near the centerline of the subject remain near the centerline of the image; objects in the far lower right corner (for ex.) of the subject field, appear in the far upper left corner of the image.

In the third, depth dimension the equation for the position of the focus is a bit more complex (it can never be closer to the lens than 1 focal length), but nearby objects in the subject focus distantly from the lens in the image, and objects far from the lens focus near 1 focal length away in the image - as close as it can get. There are equations for that, and they work well.

The Scheimpflug principle recognizes that the focal point of an object (say a small object) follows that equation, regardless of other objects in the view. So the locus (math term) of points where the surface of a horizontal roadway comes to a focus will fall on a plane that satisfies the requirement that all three planes, subject, lens center, and focal plane meet at a common point.

The figure with the Wiki posting illustrates this well. Plus, you don't need all the math and lens principles to 'get it,' and use it.

The term 'depth of field' can be taken to apply at any given point on the image plane, and I think it should be used that way. The image of a small object, viewed in 3 dimensions, forms a cone that comes to a point at the point of focus. [insert sketch here.] We calculate the depth of field as being the distance from the focal point, in the direction toward and away from the lens, at which the cone becomes a certain diameter - a certain amount out of focus, if you will. How much out of focus is a matter of convention, based on the historical capability of film and lenses. Remember:

You don't know what fuzzy is until you've seen sharp.

If you blow up a photographic image by 20X or more, you will discover that what used to appear as 'in focus' really isn't so sharp. The 'exactly in focus' points remain sharp, but the 'might as well be in-focus' points now appear less acceptable than before. With modern high end digital cameras and lenses, you can see this effect on your very own display. What you have done is reduce the allowable diameter of the cone that you call in-focus. You have reduced the depth of field.

Take a photograph of a brick wall at an angle to the wall so that only one vertical line is in focus, and as you blow it up, less and less of it will pass your 'in-focus' criterion.

When the Scheimpflug principle is used to adjust the film and lens planes and get more of the flat road into focus on the film, the depth of field, measured at each point on the image, remains the same - it is controlled by the lens aperture (in f/ stops), the focal length, and the distance of the subject. If you use a wide open lens at say f/4 (that's going to be a large view camera lens!) and adjust to get the horizontal roadway into focus, you will see that a person standing in the road has their feet in focus, but their head may be out of focus. If they are reasonably close to the camera, a smaller f/ stop will be needed to get both the road and the person's head into focus at once, and no amount of Scheimpflug adjustment will get away from that.

The Scheimpflug principle allows you to match the focal plane with the subject, in certain cases. It allows you to make a focal plane that is not parallel to the plane of the lens. It does not change the depth of field calculations, or the depth of the field of the image.

JayWarner 17:56, 16 February 2007 (UTC) Jay Warner Wisconsin, USA quality@a2q.com


 * I agree that one doesn't need all the math to effectively use tilts and swings—in the field, I don't use any calculations other than determining the f-number from the focus spread. But I don't know many people who try to envision the intersection of the object, lens, and focal planes to actually set tilts or swings. There are several common ways of doing it, but they're not really appropriate here because Wikipedia is not a “how-to” guide. The equations for the rotation axis distance, and for the relationships among tilt, image distance, object distance, and angle of the plane of focus come up frequently in discussions (often incorrectly), so it seemed reasonable to include them here. There's a lot more math that I don't think is as useful, so I left it out.


 * “So the locus (math term) of points where the surface of a horizontal roadway comes to a focus will fall on a plane that satisfies the requirement that all three planes, subject, lens center, and focal plane meet at a common point.”


 * This is essentially what's shown in the proof of the Scheimpflug principle included in the article.


 * This proof didn't exist at the time of Jay's comment; nonetheless, I've added a couple of steps to make it more obvious that the proof covers what Jay was saying. (comment added at 14:01, 16 March 2010 but not signed. JeffConrad (talk) 02:02, 17 March 2010 (UTC))


 * I don't quite follow your comments about DoF. Are you suggesting that the DoF isn't wedge shaped when the lens is tilted? That it is is well-established in sources such as Merklinger, Stroebel, and Tillmans, and has long been shown in diagrams from camera manufacturers such as Sinar and Linhof. It's also quite easily derived by several different methods. I don't think it's really disputed.


 * Along any given ray, the DoF isn't changed by tilting, as Merklinger (1996, 115–116) describes. That could be added to this article, but I thought it would be more likely to confuse than enlighten, so I left it out. In any event, the DoF limits are different for every ray, so the effect is a wedge-shaped DoF. Understanding this is key to effectively using tilt or swing for a subject that isn't planar.


 * I agree that enlargement affects DoF if the viewing distance remains the same. This is covered in the Depth of field article. I'm not quite sure how your comments relate to this article.

Jay is exactly and entirely correct, although his explanation is a bit wordy.

I fixed this article earlier, and added the needed diagram. I cannot see why the article has now been revised back to the spooky language it now has.

Fil Hunter author "Light - Science & Magic" filhunter@verizon.net


 * Fil, I have no idea what you mean by “spooky language”. And I question some of the “fixes” in your edit of 31 December 2006, such as


 * “Depth of field appears to be infinite if the entire subject is in the Scheinmpflug image plane, such as a roadway extending for miles from the camera on flat terrain. (In fact, a respected photographic publisher did, indeed, claim in the first edition of a well-selling text that the Scheimfplug Principle actually creates infinite depth of field!)”


 * What this really seems to be saying is that everything in the plane of focus is sharp, which would seem self-evident, and is not what I would call infinite DoF. And it's hardly how most other sources describe it. References such as “a respected photographic publisher” and “a well-selling text” don't exactly qualify as verifiable sources.


 * I don't understand a couple of other points:


 * “However, normal depth of field caculations also apply to Sheimpflug; the near and far limits of depth of field are tilted proportionally to the lens tilt and intersect along the same line as the lens plane and two focal planes.”


 * As I read this, it seems to say that the DoF is wedge shaped, much as the article currently reads. Strictly, I would disagree with the statement that the tilt of the planes is proportional to the lens tilt; rather, it's given by the equations for tan ψ.


 * “Sheimpflug's principle is practical only with extremely good lenses designed with the principle in mind.”


 * I take this to mean that lens tilt requires additional covering power. This certainly is true, but it's possible to employ the Scheimpflug principle using back tilt, which doesn't require additional covering power. Perhaps we could add that to this article, but I think it's more properly covered in the View camera article—rise and fall and lateral shifts also require additional covering power. JeffConrad (talk) 22:46, 15 March 2010 (UTC)

I was going through the trig trying to derive the equation for tan psi in terms of the image plane distance v' and I think there needs to  be a correction. Instead of {u'} it ought to be {v'}. i.e. tan psi = v'sin theta / v'cos theta -f. I didn't edit the page because I do not know how. Perhaps someone else could check my maths and edit it themselves if they agree? [comment by Cjrlord (talk) on 15 March 2010 at 16:01]


 * Cjrlord, your  derivation of the equation for tan ψ is   correct. But that's the way the equation currently reads. Am I missing  something in your comment? JeffConrad (talk) 13:17, 16 March 2010 (UTC)

Errors in proof
Hi, I'm new to wikipedia, so please excuse any transgressions in protocol. But I noticed what I think are some sign errors in the proof for the Scheimpflug principle and wanted to point them out. The first time magnification is defined, there is a minus sign in front of the ratio. But the third time m appears (after the phrase "On the image side of the lens, again from Figure 6") there is no minus sign. So the convention isn't consistent.

Also, looking at the last line (y_v = -(a - b/f)v + b), there is a sign error in front of the b/f term. The previous line shows that it should have the same sign as the av term. —Preceding unsigned comment added by Pixelatedcode (talk • contribs) 20:15, 4 September 2010 (UTC)


 * Protocol is to point out the error so that the idiot who made it can fix it ... I've (hopefully) fixed the errors, and attempted to explain the combination of normal Cartesian coordinates and the optical sign convention that shows object distances increasing to the left of the lens plane. See if this works. JeffConrad (talk) 02:52, 5 September 2010 (UTC)


 * Looks good to me. Also seems to match the result I got from a different proof-method I tried.  Btw, I like your proof approach.  It uses some simple geometry to make for a more straightforward and intuitive proof (my independent attempt was more algebraic).  —Preceding unsigned comment added by Pixelatedcode (talk • contribs) 19:19, 5 September 2010 (UTC)

Edits of 22–23 September 2010
I've made a couple of minor changes in attempt to clarify how the examples were calculated. I've used Merklinger's approximation for DoF on a plane parallel to the image plane because it's simple, and to my knowledge, he's the only published source. But his approximation isn't the best one for large values of tilt; specifically, as distance increases, the image distance v → f, but the line-of-sight (rail) distance v′ → f&thinsp;/&thinsp;cos&thinsp;θ, so at the hyperfocal distance, the DoF on a plane parallel to the image plane is approximately 2&thinsp;f&thinsp;/&thinsp;tan&thinsp;θ rather than 2J = 2&thinsp;f&thinsp;/&thinsp;sin&thinsp;θ. At the hyperfocal distance, the difference between v and f is negligible, but with large tilt, as may be used on a large-format camera, the difference between cos&thinsp;θ and 1 may not be negligible. As a consequence, to be strictly correct, I've used to notes to explain the differences. If this makes an already arcane concept too confusing, we could simply use the more accurate approximation and have nothing that needs explaining. The down side of course is that someone familiar with Merklinger may notice the apparent disparity and wonder which is correct. The “exact” formula that he gives on p. 126 is indeed exact, so no qualification is needed.

Though it may seem like I'm making a big deal out of a small detail, the DoF distribution on a plane parallel to the image plane is a key concept in choosing the best position for the plane of focus in a typical scene that isn't strictly planar, and to my knowledge, it had not been described prior to Merklinger, and I think his contribution here is due some deference. JeffConrad (talk) 07:45, 23 September 2010 (UTC)

Question about magnification
I'm struggling with the Angle of the PoF section. My difficulty stems from the magnification terms in the final equation. For a system with no magnification, I believe I should take $$m = -1$$, which then gives $$\tan \psi = 0$$, placing the focus plane vertical and parallel to the image plane, irrespective of the image plane angle. I may have the sign convention wrong and $$m = +1$$, this would give $$\tan \psi = 2 \tan \theta$$ whereas I would expect $$\psi = 2 \theta$$ by symmetry. I think my confusion arises because figure 6 defines the magnification differently, as $$m=-\frac{y_v}{y_u}$$ which is along the axis of the lens normal (magnification is a function of the ray angle). In figure 7 the magnification is expressed along an axis tilted with respect to the lens normal. Nick.hawkes99 (talk) 17:33, 2 March 2018 (UTC)

Incorrect to say "the PoF cannot be set to pass through more than one arbitrarily chosen point"
The statement "Of course, the tilt also affects the position of the PoF, so if the tilt is chosen to minimize the region of sharpness, the PoF cannot be set to pass through more than one arbitrarily chosen point. If the PoF is to pass through more than one arbitrary point, the tilt and focus are fixed, and the lens f-number is the only available control for adjusting sharpness." is not true in practice and unless I have misunderstood the wording, I believe this section should be revised. With swing and tilt it is possible to have what is in effect a plane of focus angled across at least three points in the depth of the space that is framed by the camera. Jamesmcardle(talk) 21:56, 4 February 2019 (UTC)