The streetlight changed colour: light pollution filters on a phone

The packaging promises a mountain sky from your balcony. Inside there is a round piece of glass held in a plastic clip, it snaps over the phone’s camera, and the label says the city light stays outside. That promise rested on serious physics for thirty years. Then two things changed: the lamps in the street, and the instrument you are clipping the filter onto. The two are unrelated, and either one on its own is enough to waste the money.

The filter was invented to fight two lines

The lamps that lit our cities until yesterday did not emit white light: they emitted lines. Low pressure sodium puts almost everything it has into the doublet at 589.0 and 589.6 nanometres, the pair that spectroscopy textbooks call the D lines. Mercury vapour adds a handful of bright ones, blue at 435.8, green at 546.1, a yellow couple around 577 and 579. Those wavelengths have been sitting in the NIST atomic databases for decades and they do not drift by a nanometre.

At that point an interference filter has an almost trivial job. Stack thin layers that reflect those lines away and let everything else through, put the glass in front of the camera, and the sky background collapses while the stars stay where they were. The signal an astrophotographer cares about happily falls elsewhere: hydrogen alpha at 656.3 nanometres, doubly ionised oxygen at 495.9 and 500.7, starlight smeared across the whole visible range. Subtract narrow, keep wide. It was arithmetic, and it worked.

Then the streetlight turned white

A white LED is built in a way that has nothing to do with lines. Take a blue emitter, coat it with a phosphor that re-emits over a very broad band, and out comes a continuous spectrum covering the visible from end to end. There is nothing narrow left in that lamp to cut.

DarkSky International puts the consequence bluntly: for the same amount of light emitted, a blue rich white LED pollutes the sky roughly two and a half times more than a high pressure sodium lamp, and the world atlas of artificial night sky brightness warned that a conversion carried out without limiting blue emission can more than double the brightness of the night sky. Field measurements agree. In 2023 Kyba and colleagues published in Science an analysis of more than fifty thousand naked eye observations gathered between 2011 and 2022 by the Globe at Night project: the loss of visible stars reported by participants is equivalent to sky brightness growing by 9.6 per cent a year.

A continuous background sits on exactly the same wavelengths as your target. Whatever band the filter decides to block, it blocks the same fraction of galaxy, cluster and Milky Way. The glass keeps doing its job with precision. The job has become pointless.

In front of a wide angle, that glass works crooked

There is a second problem, and this one is specific to phones. The passband of an interference filter depends on the angle at which light crosses it. Every optics manufacturer writes the rule the same way, Edmund Optics included: the wavelength shifts as the square root of one minus the squared sine of the angle divided by the effective index of the coating stack, and that index typically sits between 1.5 and 2.5. Off axis, the band always slides towards the blue.

On a telescope you run the numbers on the light cone, and it already bites there: Astronomik specifies its CLS-CCD for focal ratios of f/3 and slower, which are fairly gentle cones. A phone’s main camera sits around f/1.8. The real trouble, though, comes from the clip sitting in front of the lens rather than behind it: that glass does not see the cone from a single point, it sees the entire framed field. A 24 millimetre equivalent lens covers about 74 degrees horizontally, so at the edges light hits the filter 37 degrees off axis, and in the corners more than 40. Your ultrawide, which spans over a hundred degrees, is in far worse shape.

The calculation is quick and worth doing. With an effective index of 2, a band centred on hydrogen alpha at 656 nanometres in the middle of the frame measures about 626 at the edge: thirty nanometres of slide, when narrowband filters are sold in six and twelve nanometre widths. The edge of your frame is getting a different filter from the one you bought. On a broadband CLS type filter, whose transition sits around 590 nanometres, that threshold drops below 565 at the edge and starts eating green.

You see the result before anything else: a colour cast that changes from centre to corner, which means a photograph where white balance has no single solution, because no correction fixes the whole frame at once. Stacking a hundred frames changes nothing. The gradient is identical in all hundred, so it survives the average untouched.

The photon budget closes in the red

Then comes the simplest argument, the one you can do with two fractions. Call s the share of signal the filter lets through and b the share of sky background. When background photon noise is in charge, signal to noise moves as s divided by the square root of b.

Under the old lamps the deal was generous. A filter cutting two thirds of a background concentrated in a few lines while passing nine tenths of the signal would take the ratio to one and a half times where it started, better than half a stop gained for free. With a continuous background s and b look alike, the ratio collapses to the square root of s, and whatever the filter takes away you pay for. Cut half the light to keep out half the city and you are left with 70 per cent of the signal to noise you had, for the same number of frames. Getting it back means doubling your exposures, and a cold battery is not interested in the discussion.

Where glass still earns its keep, and it is not here

The wrong filter is not a bad filter: it is a tool designed for different optics. Narrowband on hydrogen alpha and oxygen, mounted behind a slow lens on a mount that tracks, is still the best way to shoot emission nebulae from inside a city, because there the target really does emit in lines and the continuous background can be butchered without mercy. At the eyepiece, a UHC or an OIII on a planetary nebula still does something close to magic.

And then there is the one filter that is mandatory rather than optional on a phone, the certified solar one, which is there to keep your sensor and your eyes alive. You buy that, you inspect it before every use, and nothing substitutes for it.

What actually works instead of glass

Against a sky lit by a continuous spectrum, four moves remain, all of them better than an accessory. Distance first: half an hour of driving towards a sky one class darker beats any piece of glass, and the Bortle scale tells you how much you are gaining before you even set off. Then altitude: aim high and turn your back on the city’s dome of light and you push less illuminated air through your line of sight, since at thirty degrees above the horizon you are looking through twice as much of it as at the zenith.

Third, the number of frames. Background noise falls with the square root of how many you stack, and three hundred eight second exposures handle skyglow better than any filter, with the advantage of not stealing a single photon from the target. Fourth, the gradient comes out afterwards, in processing, where a properly subtracted sky model cleans up what the glass would merely have tinted differently.

One physical thing is worth building: a shade. When the streetlight is outside the frame but its light still lands on the front element, a folded piece of black card kills reflections and haloes that no filter can touch, because that light is exactly what the filter has to pass when it arrives from the stars.

The right glass against a modern streetlight does exist, it is sold everywhere and it is cheap. It is called a kilometre.