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I need to take overhead top view pictures of a stationary gas compressor. How can I get the image to appear flat by adjusting the focal length? Example: I need to know what type of lense or camera to purchase to take a picture of a gods eye view of a machine without being far above the machine. I want to be able to scale the image without the perspective effects or lensing that occurs from a longer focal length.
Any suggestions?
Perspective is determined by camera position, not focal length. The reason many people think focal length is the determining factor is because one must get much closer to a subject with a short focal length lens than one must get with a long focal length lens if one wants to fill the frame with the subject. But it is the subject distance that is actually the determining factor in perspective.
If your compressor is 10 meters tall and your camera is 10 meters above the top of the compressor, the bottom of the compressor will be twice as far from the camera as the top of the compressor is. Items at the bottom of the compressor will look half as wide as the same size item at the top of the compressor.
To get what we consider the 'normal' perspective of an object, we tend to use a focal length that either matches or is a bit longer than the diagonal of the sensor. That is, if we use a 36x24mm full frame camera with a diagonal of 43.3 mm, then we use a roughly 45-50mm lens. This gives us an angle of view that requires us to be slightly more than twice as far from an object we are imaging as the maximum width/height of the object. If we are imaging an object that is four feet wide and four feet high, we need to back up a little more than eight feet to capture it with a normal lens.
The type of projection a lens uses to represent a three-dimensional world on a two dimensional image plane can also result in what we call geometric distortion. But this is different from the perspective distortion that results from a very close or very far camera position.
To get a view where objects on the far end of a three dimensional subject appear the same size as objects on the near side of the subject, we must use a telecentric type lens that will give us an orthographic view of our subject. One of the basic requirements of a telecentric lens is that the lens must be at least as large in diameter as the subject. That tends to make them very expensive. Unless you have a budget that matches or even exceeds the military budget of a small country, or unless your gas compressor is very small, it's doubtful you could consider a telecentric lens for your project.
Another solution to get an approximate orthographic view is to use a linear motion scan camera¹ (a/k/a parallel motion scan camera) or use a more typical camera to produce a panorama where each shot is taken from a different position opposite the subject's width.
¹ Typically, the object being photographed is moved past the sanning camera at a constant speed, but the obverse can also be the case, such as with aerial or satellite camera platforms that image the surface of the earth as they pass over it.
The only possible answer about a lens is that standing farther away and using a longer lens will be more "flat" than the opposite. Standing close with a short lens would be the worst possible answer. The farther the distance (and therefore the longer lens to magnify it), the flatter the perspective appears.
However, for like a portrait of a human face, 6 to 10 feet distance (a couple of meters) is considered very acceptable for a proper and acceptable perspective view (simply then looks like what we are familiar with seeing). But size still varies with distance, so your compressor requirement (seeking very flat) needs much more distance.
Suppose your compressor is 3 feet tall, meaning if you stand 5 feet away, some parts are at 5 and some parts are at 8 feet. Objects at 8 feet will always be seen smaller than objects at 5 feet. But if you stand 100 feet away, now some parts are 100 feet, and some are 103 feet distant. That would be a very small size difference, which might be called negligible and flat. This is the effect of a longer lens (makes things appear more flat), but that difference is entirely due to the distance, not the lens. But no matter at what distance you stand, there is always that 3 foot difference.
The Rule is: Perspective effects depend only on the distance, NOT on the lens used. That is, perspective depends only on where you stand to view it (i.e., the distance to it). Wherever you stand, all your lens can see is the view seen from that spot. Objects more distant will appear smaller than objects that are closer. That is simply how distance works, and we call it Perspective.
The apparent size is not linear with distance, it varies with with the tangent of the subtended angle, which can be far from linear. Seen up close, the angle is large, causing a large effect. But as the angle becomes small (say less than 10 degrees, the difference approximates becoming linear (however, farther is still always smaller than closer).
To make the angle of size become small requires viewing from a greater distance... which then also makes the size seem small...
so to view it larger then requires the magnification of a longer lens. But the size and angle and perspective depends on the distance, NOT on the lens standing at that distance.
Any lens merely shows what it sees from that location. There is nothing else a lens can do but to show what it sees. What it sees (the perspective) depends on where you stand to view the scene (i.e., depends only on the distance to the various objects in the scene).
So if you need to show proper proportional views, it sounds like you need to show additional views from more angles (subject objects being at more the SAME distance) to properly show all aspects of size. Maybe also include a spec chart of the dimensions of various parts of it.
A software tool like Hugin (free open source tool) should allow you to take several photos of the compressors from relatively close overhead (i.e. at head height above the left hand side, the middle and then the right hand side of the compressor, as seen from above) and then merge them together seamlessly into a single "panorama". So long as you overlap each source image by about 30%, Hugin is pretty good at merging.
Then choose something like a "Rectilinear Projection" for the output image and you should have exactly what you're after:
The rectilinear projection also has the fundamental property that straight lines in real 3D space are mapped to straight lines in the projected image.*
There is no distance that will give you a "plan view" of a 3 dimensional object using lens imaging practically speaking.
The further away you are from the object will tend to minimize the visual effect of perspective.
It cannot be eliminated using "normal" photographical equipment (f-theta lenses notwithstanding) in a "studio" setting.
The Workaround:
When it is impractical to use vertical distance to achieve the intended visual effect, reposition the subject to allow sufficient horizontal distance to approximate the distance-flattening desired. In other words, tip the subject 90° and use sufficient horizontal distance to achieve the desired effect. You will have more control for fine-tuning your camera position and lighting.
