# Galaxies Writ Small

 Courtesy imgur user ScienceLlama

At a glance, it’s easy to tell that something’s not right with the galaxies and clusters in these images from deep space, but it might sound silly when it’s put into words: they’re little! The photographic technique of miniature faking takes advantage of the way light is focused by a lens to trick your brain into perceiving something that’s thousands of light-years across as being small enough to fit into the palm of your hand.
If you know anything about photography, optics, or burning things with a magnifying glass, you know that any lens has a certain focal length determined by its shape. If you hold a lens above the sidewalk at that distance, you can see the sun projected in miniature onto the pavement. Move it up or down, and the image shrinks or grows, blurring in the process. Human vision works in a similar way, with muscles that change the shape of your lens so that light from a certain distance will form a coherent image on the retina. A mechanical zoom function uses a series of small lenses to achieve this same effect, bringing all objects at a certain distance from the camera into sharp focus, while letting the foreground and background blur.
 Courtesy imgur user ScienceLlama
Mathematically, there is only a single plane, exactly at the focal distance, which is perfectly sharp in the image created by a lens. All points of light outside this plane come in as diffuse circles, like you see at the lower and upper edges of the image above. However, we only begin to see them as circles once they are sufficiently far from the plane of focus (a concept known amusingly as the circle of confusion); if your eyes were focused at a spot 5.5 meters away, you might still be able to read a poster as long as it’s between 5 and 6 meters from you. In a photograph, the range of distances at which you can clearly make out an object is called the depth of field, and it is by toying with this property that we get the shrink-ray effect seen in miniature faking.
The depth of field is given by the following relation:
 Math courtesy of Wikipedia, where they do the derivation if you don’t trust us.
N and c are related, respectively, to aperture size and to how unfocused a point has to be before it starts to look “blurry”. M is the magnification factor, which is the critical variable here. If you’re taking an image that’s going to turn out smaller than the object (as you’re bound to, with a galaxy), M is less than 1, so it’s easy to get the entire thing in focus. But for values of M greater than 1, the DOF shrinks rapidly, and you’re only able to see things sharply if they’re very near the focal plane.
Courtesy imgur user ScienceLlama
Since the values of N and c don’t really change, the brain can rely on depth of field to tell you whether you’re looking at something small and close-up or large and far away, in the absence of other visual distance cues like parallax. By selecting a focal plane in the image, and adding artificial blur effects outside that region, the artist makes it seem as though the depth of field is very small. (The illusion is far older than Photoshop, though, and is still well-known by its analog name, tilt-shift photography.) From there, the magic happens entirely in your head: without any conscious thought, our brains solve for M in a rearranged version of the equation above. Since we see a small DOF and instinctively know our own values of N (based on your pupil size) and c (based on the density of rods and cones in your retina), it’s only natural to conclude that M must be great, so we must have here a pocket-sized nebula. Enjoy the photo set, secure in the knowledge that if anyone asks what you’re up to, you can tell them: “algebra”.
 Check out ScienceLlama‘s page for more from this gallery!