note on perspective

 Posts: 801
 Joined: Wed Jan 07, 2015 2:10 pm
note on perspective
Perspective is sometimes used in holography (with respect to the arrangement of the sculpture or objects). An impression of far greater depth can be given this way. The attached photos show how a "room" is put into perspective, with foreshortened squares on the floor, walls, and ceiling. The "real" room would be 60mm in depth, but the foreshortened room only needs to be 30mm.
note on perspective
Hello Joe,
That's quite an effect and a good presentation. The short sides of the tiles seem to get smaller and smaller, like a geometric series. But the diagonals show that they have the same size. The diagonals are a bit confusing to me though since they either begin or end at the corners but not both, so they document the uniform size only for a part of the wall tiles.
With more tiles, would the depth effect get more pronounced or is the example given close to the useful limit? I had the impression of a slight distortion of the geometry on the first picture, which prompted the idea that the appearance of distortion could also be achieved on purpose by using other shapes/sizes for the tiles.
That's quite an effect and a good presentation. The short sides of the tiles seem to get smaller and smaller, like a geometric series. But the diagonals show that they have the same size. The diagonals are a bit confusing to me though since they either begin or end at the corners but not both, so they document the uniform size only for a part of the wall tiles.
With more tiles, would the depth effect get more pronounced or is the example given close to the useful limit? I had the impression of a slight distortion of the geometry on the first picture, which prompted the idea that the appearance of distortion could also be achieved on purpose by using other shapes/sizes for the tiles.

 Posts: 801
 Joined: Wed Jan 07, 2015 2:10 pm
note on perspective
That's a very good point about the distortion apparent in the first picture  the perspective doesn't look quite right, does it? But I think the explanation is simple.
Perspective is notorious for being difficult to explain, and the more it's put into words, it seems the more confusing it gets. The best thing is to do a few tests. But I will give it a try.
It may help for people with a background in holography or optics to think of "forced perspective" in terms of raytracing. A number of things need to be determined precisely before a perspective construction can be made. One important thing which might be overlooked is the precise location of the eye with respect to the "picture plane" (i.e., emulsion). In the above "room" the eye was determined to be exactly 25mm above "ground level" and exactly 8 inches from the picture plane. The picture plane is determined to be exactly 70mm wide X 50mm tall, which is the front openend of the box. (The picture plane is thus divided into 5mm squares, 14 squares wide and 10 squares tall.) The depth of the "represented" scene needs to be determined also, in this case it's 60mm or 12 squares. Lastly, the amount of foreshortening needs to be established. A simple way of doing this is to determine how much the "floor" will be raised, in degrees. In the above example, it's raised at a 5 degree angle.
Once all of these factors are determined, then the raytracing can begin, with a side view of the arrangement on paper. This would show the position of the eye, the 8 inch distance to the picture plane, the picture plane, and the "unforeshortened" groundplan or floor, which is 60mm deep. If a ray is traced from the eye to the termination of floor (which is 60mm deep), it will intersect the picture plane at a certain point. If an angled floor line is drawn, say at 5 degrees "up," then that same point on the picture plane will determine the depth of the "foreshortened" floor. In the above case, the foreshortened floor is halved in size to about 30mm "real" depth (60mm apparent depth).
Now, the probable reason why the first photo looks distorted is that the photo was taken far too close to the "picture plane" (i.e, the front of the box). It was just a few inches, because if the camera was all the way back to the "correct" viewing distance of 8 inches, the lines wouldn't show up in the photograph. An 8 inch distance is pretty close to the limit where many of us can focus our eyes.
Perspective only provides a true "illusion" when the eye is at an exact position in space, and the perspective is constructed with this in mind. As the eye moves away from this distance, the perspective becomes more and more distorted. However, with holograms, it's a very worthwhile tradeoff, because the scene is limited to a frontview, and "real depth" is at a premium (laser power, coherence, etc.).
As you noticed, the diagonals are important. Perfect squares need to be determined somewhere in the scene, then diagonals need to be drawn to establish the correct spacing of other squares. A person needs to become like Sherlock Holmes, and deduce where lines "must" be located. Once the floor, ceiling, and walls have been foreshortened with squares, then any object in the room may be foreshortened by using the corresponding floor, wall, and ceiling squares as a guide, noting particularly where these lines intersect in space (in the room's interior). With regards to the degree of foreshortening applied, any amount can be used, but as the amount goes up (say a 10 degree floor inclination) the more obvious the distortions will be when the eye moves away from the correct position. However, when the eye is in the correct position, and the perspective is done properly, the scene will be pretty much "exactly" the same thing as the real scene.
Probably, what I said above makes little sense. Perspective is extremely difficult to explain, even with words, pictures, and demonstration.
Perspective is notorious for being difficult to explain, and the more it's put into words, it seems the more confusing it gets. The best thing is to do a few tests. But I will give it a try.
It may help for people with a background in holography or optics to think of "forced perspective" in terms of raytracing. A number of things need to be determined precisely before a perspective construction can be made. One important thing which might be overlooked is the precise location of the eye with respect to the "picture plane" (i.e., emulsion). In the above "room" the eye was determined to be exactly 25mm above "ground level" and exactly 8 inches from the picture plane. The picture plane is determined to be exactly 70mm wide X 50mm tall, which is the front openend of the box. (The picture plane is thus divided into 5mm squares, 14 squares wide and 10 squares tall.) The depth of the "represented" scene needs to be determined also, in this case it's 60mm or 12 squares. Lastly, the amount of foreshortening needs to be established. A simple way of doing this is to determine how much the "floor" will be raised, in degrees. In the above example, it's raised at a 5 degree angle.
Once all of these factors are determined, then the raytracing can begin, with a side view of the arrangement on paper. This would show the position of the eye, the 8 inch distance to the picture plane, the picture plane, and the "unforeshortened" groundplan or floor, which is 60mm deep. If a ray is traced from the eye to the termination of floor (which is 60mm deep), it will intersect the picture plane at a certain point. If an angled floor line is drawn, say at 5 degrees "up," then that same point on the picture plane will determine the depth of the "foreshortened" floor. In the above case, the foreshortened floor is halved in size to about 30mm "real" depth (60mm apparent depth).
Now, the probable reason why the first photo looks distorted is that the photo was taken far too close to the "picture plane" (i.e, the front of the box). It was just a few inches, because if the camera was all the way back to the "correct" viewing distance of 8 inches, the lines wouldn't show up in the photograph. An 8 inch distance is pretty close to the limit where many of us can focus our eyes.
Perspective only provides a true "illusion" when the eye is at an exact position in space, and the perspective is constructed with this in mind. As the eye moves away from this distance, the perspective becomes more and more distorted. However, with holograms, it's a very worthwhile tradeoff, because the scene is limited to a frontview, and "real depth" is at a premium (laser power, coherence, etc.).
As you noticed, the diagonals are important. Perfect squares need to be determined somewhere in the scene, then diagonals need to be drawn to establish the correct spacing of other squares. A person needs to become like Sherlock Holmes, and deduce where lines "must" be located. Once the floor, ceiling, and walls have been foreshortened with squares, then any object in the room may be foreshortened by using the corresponding floor, wall, and ceiling squares as a guide, noting particularly where these lines intersect in space (in the room's interior). With regards to the degree of foreshortening applied, any amount can be used, but as the amount goes up (say a 10 degree floor inclination) the more obvious the distortions will be when the eye moves away from the correct position. However, when the eye is in the correct position, and the perspective is done properly, the scene will be pretty much "exactly" the same thing as the real scene.
Probably, what I said above makes little sense. Perspective is extremely difficult to explain, even with words, pictures, and demonstration.

 Posts: 801
 Joined: Wed Jan 07, 2015 2:10 pm
note on perspective
I've attached a page from the book by Andrea Pozzo (1693) which shows some basics of his method. The subject to be foreshortened is a pair of column bases. On the left are the "unforeshortened" plan and elevation of the subject. To the bottom, under the "floor," is the foreshortened plan. To the left, on the "wall" is the foreshortened elevation. Once these are in position, lines may be drawn (as indicated in the drawing) to show where points intersect in space.
 Attachments

 pozzo389.pdf
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Re: note on perspective
Perspective as applied to holography is a very interesting subject, but there isn’t much analysis and experiments on this. I never tried perspective tests with analog holography, but I did several experiments with perspective in synthetic holograms (CGH). Around 2000 2003, I made a few holograms using perspective grids to measure distortions, depth of field, size and distance consistency, etc. Some distortions that are well known in artificial perspective are solved by the multiple angle of view and the optical process of synthetic holography. However, other kinds of distortions appear. For example, shapes will stretch on the x or y axis depending on the viewing distance. This is also different depending if you have a full parallax hologram or horizontal parallax only. There’s a lot to do on this subject since CGH could be the grail searched by centuries of perspectivists.
As for accelerated perspective, that would be an interesting experiment in CGH. Basically, it should result in the same depth illusion, if and only if the viewer looks at the hologram from a single point of view. But then, what would be the point? Isn’t that a contradiction with the purpose of holography?
Here are some images I used in my experiments. Sorry I can’t find the bad photos I have of the holograms that were made with these images... If I find them, I will post them.
As for accelerated perspective, that would be an interesting experiment in CGH. Basically, it should result in the same depth illusion, if and only if the viewer looks at the hologram from a single point of view. But then, what would be the point? Isn’t that a contradiction with the purpose of holography?
Here are some images I used in my experiments. Sorry I can’t find the bad photos I have of the holograms that were made with these images... If I find them, I will post them.
Re: note on perspective
This is an effect of magnification/distortion along the x or y axis. Specifically, the variation dx(i)/dx(o), x(i) is the recon viewpoint and x(o) is the "object" viewpoint.. Take a look at section 5 ( http://www.tripletake.com/publications ... graphy.pdf ). Notice, in particular, that if the hologram is viewed in white light, then mu is not unity, thus increasing this distortion.jacques wrote:However, other kinds of distortions appear. For example, shapes will stretch on the x or y axis depending on the viewing distance. This is also different depending if you have a full parallax hologram or horizontal parallax only. There’s a lot to do on this subject since CGH could be the grail searched by centuries of perspectivists.