# Why are filter flare images centrally inverted?

A previous question asked about the origin of the ghost-like image of the fluorescent bulb on this image,

which turns out to be something called a filter flare, of which there are more examples here and here, and which is explained in this page as being caused by a combination of two reflections, one on the camera's sensor and then one on a filter (or any other flat optical element), probably outwards from the lens:

Image source, © Paul van Walree

I am specifically confused about why the 'ghost' image appears inverted (i.e. rotated by 180°); since it has undergone two reflections (with each one causing an inversion), naively, it should appear in the same orientation as the original image. Doing some rough additional ray tracings on the diagram above I can roughly see that the mirror image should indeed be inverted, but I'm struggling to square that with the rough heuristics that each reflection should cause an inversion. So what gives?

• Isn't that because the ghost image is reflected only once w.r.t the image formed? (but twice w.r.t the actual object being photographed) – Mostafa Jan 7 '17 at 23:49
• Did you even have a filter on the camera when you took this picture? Or are you referring to "filter flare" in the generic sense (i.e., lens flare)? I think that it's difficult to try to analyze and explain lens flare images for most modern lenses because unlike your drawing they actually may have lots of individual glass lens elements. My Nikon F/2.8 70-200mm lens has 21 separate glass elements in it. Try to ray-trace analyze that and determine what the flare image looks like. Even "simple" lenses such as a Nikon 50 mm f/1.8 may have 5 elements and can be very difficult to analyze for flare. – user93237 Jan 8 '17 at 1:05
• @SamuelWeir The picture is clearly attributed and was not taken by me; why are you assuming that it was? In any case, the question is about the general phenomenon as displayed in the multiple examples I linked to and not to any single instance. – Emilio Pisanty Jan 8 '17 at 1:07
• @Elilio Pisanty - OK, I see the attribution now. The fact is that lens flare does not require that a filter be in place and is not necessarily due to reflection off the sensor/film. There are lots of glass elements in a typical lens. – user93237 Jan 8 '17 at 1:08
• @SamuelWeir (a) I would appreciate a correct spelling of my name, (b) you obviously still haven't seen the attribution or you would understand that I neither took the picture, nor know whether it did or didn't employ a filter, and indeed if you had followed the link you would have seen (c) me asking precisely that question of the photographer, which is as yet unanswered. And, I stress again, (d) my question here is not about any one picture but the phenomenon in general, so I don't see how your question is pertinent. – Emilio Pisanty Jan 8 '17 at 1:12

It's only undergone one reflection: the film/sensor is not reflecting the image, but serving as a source of light for the optical system: look at the blue light rays which make this clear, and would be insane in terms of reflections). The ghost results from diffuse rather than specular reflection in other words: light scattering from the film/sensor. Additionally just look at the emulsion side of film: it is not shiny.

• Sorry, but this makes no sense: of course the film (/sensor) is causing a reflection. As appealing as it is to thing that the light goes along the black arrows and then back along the same ray with the blue arrows, that's not what happens - instead, a ray an angle $\theta$ above the horizontal will come out at angle $-\theta$. – Emilio Pisanty Jan 8 '17 at 0:54
• The photo.se question I linked to also makes it clear that this is an issue specifically with digital sensors and not with film, as the former are much more reflective than the latter; indeed, the answer clearly attributes filter flares as "what happens when you use a lens designed in the film era with a digital DSLR". Thus your final sentence is also off the mark. – Emilio Pisanty Jan 8 '17 at 0:57
• @EmilioPisanty Then I leave it up to you how to explain the inversion: perhaps it happens by magic? – tfb Jan 8 '17 at 1:40
• @EmilioPisanty I'm skeptical of whether the explanation you linked to is correct, but if that explanation is correct then this answer is correct. The blue arrows represent a diffuse reflection from the sensor, not a specular one. The claim in your linked page is not that the sensor acts as a mirror (which indeed would invert the image) but that it acts as a white screen on which the image is projected; the ghost is claimed to be an image of that image, as it were. – Nathaniel Jan 8 '17 at 4:48
• @EmilioPisanty no, I'm not handwaving, and your first comment is a misinterpretation of what the diagram is trying to indicate. It's a diffuse reflection, so the rays don't just come out at angle $-\theta$ but at all angles. If they came out at $-\theta$ then most of them would just hit the lens casing. – Nathaniel Jan 8 '17 at 10:03

Don't forget that reflection is not the only process that causes inversion. In this system of two reflectors and a positive lens between them there are 4 inversions before the ghost image is formed:

1. focusing by the lens after initial crossing of the filter,
2. reflection from the sensor,
3. reflection from the filter
4. focusing by the lens, which forms the ghost image on the sensor.

Between steps 2 and 3 there's no inversion, because the rays crossing the lens are defocused and intercepted by the filter before they form an image. It's the crossing of the rays that forms an image and results in inversion on focusing, and here it doesn't happen.

As 4 is an even number, the ghost image is upright—with respect to the object—and thus inverted with respect to the normal image.