Long Exposure and Night

The Milky Way stands over a dark ridge, and the camera sits on the carbon-fibre tripod with the Tamron 16-30mm f/2.8 Di III VXD G2 at 16 mm and f/2.8. You set 30 s, wait, then zoom in. Near the middle of the frame each star is a short dash about six pixels long. Nothing shook. The Earth turned while the shutter was open, and the 30 s setting really lasted 32 s (p. 669).

Long exposures raise three problems short ones never meet: the subject drifts across the sensor, the sensor gathers heat as well as light, and the ordinary shutter speeds stop at 30 s. Each has an arithmetic answer, and neutral density (ND) filters, grey glass that dims every colour equally, bring the same long exposures to daylight. Page numbers in parentheses point to Nikon's Z6III Reference Guide, edition 09, which matches firmware 2.00.

01.Why Stars Become Dashes

How Fast the Sky Turns

The Earth turns once relative to the stars every 86,164 s, a sidereal day. A full turn is $2\pi$ radians, a radian being the angle whose arc equals its radius, so the sky's angular speed $\omega$ is

$$\omega = \frac{2\pi}{86{,}164\ \text{s}} \approx 7.29 \times 10^{-5}\ \text{rad/s}$$

about 15 arcseconds each second, an arcsecond being one 3600th of a degree. That is astronomy, not Nikon. A star on the celestial equator, the circle of sky above the Earth's equator, moves at the full rate. A star at declination $\delta$, its angle north or south of that circle, moves at $\omega\cos\delta$, so one at $60^\circ$ moves half as fast and Polaris, near the pole, barely moves.

From Turning Sky to Pixels

A lens of focal length $f$ turns a small angle $\theta$, in radians, into a distance $f\theta$ on the sensor. In an exposure of $t$ seconds a star's image slides

$$s = f\,\omega\,t\cos\delta$$

At 16 mm on the equator that is $16 \times 7.29 \times 10^{-5} \approx 0.00117$ mm each second. To convert to pixels, divide by the pixel pitch, the spacing of the photosites. The sensor is 35.9 mm wide (p. 997) and a full-size picture in FX, Nikon's name for the full-frame format, is 6048 pixels across (p. 998), so my estimate of the pitch is

$$p = \frac{35.9\ \text{mm}}{6048} \approx 0.00594\ \text{mm}$$

or 5.94 micrometres. The star crosses $0.00117 / 0.00594 \approx 0.197$ pixel per second, one pixel every 5.1 s, so the opening scene's 32 s gives $32 \times 0.197 \approx 6.3$ pixels. At 24 mm the same 32 s gives 9.4 pixels.

What the Rules of Thumb Assume

Turned around, the formula gives the longest exposure that keeps a trail under $k$ pixels:

$$t_{\max} = \frac{k\,p}{f\,\omega\cos\delta} \approx \frac{81\,k}{f\cos\delta}$$

with $f$ in millimetres and $t_{\max}$ in seconds, since $p/\omega \approx 81$. At 16 mm a two-pixel limit gives $81 \times 2/16 \approx 10$ s.

These figures hold near the middle of the frame. A rectilinear lens, the ordinary kind that keeps straight lines straight, stretches motion away from its axis. At 16 mm the left and right edges of a horizontal frame sit $\varphi = \arctan(17.95/16) \approx 48^\circ$ off axis, so a trail there runs $1/\cos\varphi \approx 1.5$ times longer if it lies along the edge and $1/\cos^2\varphi \approx 2.3$ times longer if it points towards the centre.

The popular 500 rule divides 500 by the focal length, 31 s at 16 mm. In the formula the focal length cancels: $s = 500\,\omega \approx 0.0365$ mm, about 6.1 pixels at any focal length. The rule dates from film, and at 100 per cent on this sensor it allows six-pixel dashes. Both are approximations, and the trail you accept depends on how large you print.

02.Heat, Hot Pixels and the Dark Frame

A photosite cannot tell light from heat. Heat in the silicon frees electrons even in darkness, called dark current, and the total grows with temperature and time. Over minutes it adds a faint glow, and a few photosites that leak far faster than the rest, hot pixels, become bright dots. Nikon lists bright spots, random bright pixels and fog in long exposures (p. 148), ties them to heat inside the camera, says they show more at high ISO, and suggests switching off between uses (p. 915).

Subtracting a Closed-Shutter Frame

The classic remedy is the dark frame: a second exposure of the same length with the shutter closed, which records the heat alone and is subtracted pixel by pixel. Nikon does not describe its method, so this is the general technique, not the Z6III's firmware.

With invented numbers, take a 60 s exposure. An ordinary photosite collects 400 electrons of starlight plus 30 of dark current. A hot one collects 400 plus 900, shows 1300 and stands out. The dark frame records 30 and 900, and subtraction leaves 400 in both.

The cost is noise. Dark current arrives at random, and its spread is the square root of its average, so 900 electrons carry a spread of $\sqrt{900} = 30$. The dark frame has its own independent spread of 30, and independent spreads add as squares, giving $\sqrt{30^2 + 30^2} \approx 42$. The pattern goes, the randomness grows a little, and the hot pixel is no longer a dot.

Long Exposure NR

Long exposure NR, NR meaning noise reduction, is OFF by default and at ON treats bright spots and fog in pictures slower than 1 s (pp. 447, 475). It runs after the shot, with a message in the display and Job NR flashing on the control panel, and no picture can be taken until it ends. Nikon says recording takes roughly twice as long, and for Bulb, Time or speeds slower than 30 s a countdown shows on the control panel (p. 475). If the wait turns out about as long as the exposure, that fits a dark frame, but Nikon names neither the method nor the length of the wait.

Switch off before the countdown ends and the picture is saved unprocessed (p. 475). ON is also Nikon's cure for uneven shading in Bulb and Time exposures (p. 916), and the first suspect when recording seems slow (p. 914). For unexpected bright spots in general, Nikon offers Pixel mapping in the setup menu (p. 834).

03.Longer Than the Standard Range

In S and M the timed speeds run from 1/8000 s to 30 s (pp. 140, 142), as Exposure Modes explains. Longer exposures need M.

Extended Shutter Speeds

Custom Setting d7 Extended shutter speeds (M), OFF by default (p. 624), adds timed speeds in M down to 900 s, fifteen minutes (pp. 669, 1000), and past 30 s the control panel counts down the time left (p. 669). The specifications offer steps of 1/3, 1/2 or 1 stop across the shutter range that d7 extends (p. 1000), a stop being a halving or doubling of the light. Pixel shift fixes d7 at OFF (p. 558), and video has its own g11 Extended shutter speeds (S/M) (pp. 629, 769).

Nikon gives the 15 s and 30 s settings as really 16 s and 32 s, matching again from 60 s on (pp. 145, 669). That is $32/30 \approx 1.067$, under a tenth of a stop of exposure, but 6.7 per cent more star trail.

Bulb and Time

Bulb and Time lie past the slowest timed speed on the main command dial, in M only (pp. 146-147). Bulb holds the shutter open while the release is held. Time opens it with one full press and closes it with a second, showing the elapsed time on the control panel. The exposure indicators vanish at both (p. 147). Nikon recommends a tripod, a remote cord or a wireless remote, and notes that its ML-L7 remote acts as Time even at Bulb (p. 148).

I own no Nikon remote. A finger on the release for minutes moves the camera throughout, and Time's two presses each nudge the tripod. So I use d7's timed speeds up to fifteen minutes, started by the self-timer, and keep Time for anything longer. Nikon does not say whether the self-timer works with Bulb or Time.

Bulb and Time cannot be combined with the interval timer (p. 531), time-lapse video (p. 541), HDR (high dynamic range) overlay (p. 521), focus shift (p. 550), auto capture (p. 577) or pixel shift (p. 558). If Bulb or Time flashes in mode S, the shutter will not release until you change the speed or select M (pp. 913, 923).

Keeping the Camera Still

Pressing the release shakes a tripod briefly. I use the self-timer at 2 s with one shot, and Silent Shooting, Timers and Time-Lapse covers it with d5 Exposure delay mode, which waits about 0.2 to 3 s after the press (p. 667). Custom Setting d6 Shutter type at its default Auto uses the electronic front-curtain shutter (EFCS), which starts the exposure electronically rather than with a moving curtain, to cut blur at slow speeds (pp. 624, 668), as Shutter Types, Rolling Shutter and Flicker explains.

For vibration reduction (VR), Nikon's stabilisation, Nikon recommends Normal or Sport on a tripod but allows that Off may suit some tripods (p. 498). As Vibration Reduction suggests, I make a frame each way and keep the sharper at 100 per cent.

04.Seeing in the Dark

Starlight View

Under a moonless sky the view through the lens is nearly black. Custom Setting d11 Starlight view (photo Lv), Lv meaning live view, brightens the display for composing, at the price of slightly jerky motion and no histogram (p. 675). It is OFF by default (p. 624), and Nikon suggests it for low-light focusing, in photo mode only (p. 122). In my setup the video record button toggles it in photo mode, where offered, as Custom Controls records.

Warm Display Colors

Eyes take many minutes to adapt to the dark, and the rod cells that see at night respond least to red, so a dim warm display spares night vision. That is general physiology, not Nikon's claim. Custom Setting d12 Warm display colors applies the idea for astronomy (p. 676).

Under Warm display color options, Mode 1 warms the shooting display, menus and playback, while Mode 2 warms the menus and the icons and text but leaves the view through the lens and the pictures true. Warm color display brightness sets the level, higher being brighter (p. 676). The defaults are Off and 0 (p. 625), and the item can go in the photo and video i menus (pp. 701, 746). I would compose in Mode 1 at low brightness and use Mode 2 when judging colour. Nikon does not say how d12 combines with d11, so try the pair at home first.

05.Long Exposures by Day With ND Filters

Stops and Powers of Two

A stop halves or doubles the light, and EV, short for exposure value, counts the same steps. Three stops of ND pass $2^{-3} = 1/8$ of the light, seven stops $2^{-7} = 1/128$. To compensate, the shutter time $t$ grows by the filter factor $2^n$ for an $n$-stop filter:

$$t_{\text{filter}} = t \times 2^{n}$$

Both examples use seven stops at 24 mm, for the reason given under the variable ND below. A waterfall metered at 1/125 s and f/11 needs $128/125 \approx 1.02$ s, and the 1 s setting is $\log_2 1.024 \approx 0.03$ stop short. Drops become a smooth sheet. From 1/2 s at dusk, seven stops give $128/2 = 64$ s, which needs M with d7, where 60 s is $\log_2(64/60) \approx 0.09$ stop short.

Metering Through a Filter

The meter reads light after the filter. Nikon recommends Center-weighted metering with any filter whose factor is above 1, as matrix metering may misjudge (pp. 487, 970). It gives 75 per cent of its weight to a central circle 12 mm or 8 mm across (p. 1001), and I use it with an ND or polariser in A mode for landscapes, as Metering records. Filters can also cause ghosting near bright lights (p. 970).

The meter's range is −4 to +17 EV at ISO 100 with an f/2 lens at 20 °C (p. 1001), and the displays flash beyond its limits (p. 145). If a strong filter in dim light goes below that, meter without it and multiply by the factor. A variable ND without marks in stops has no known factor, so meter through it.

Why a Variable ND Can Darken Unevenly

A variable ND is two polarisers, the front one turning. A polariser passes light vibrating in one direction, so an ideal first layer passes half of ordinary daylight, one stop. The second passes a share $\cos^2\theta$ of the rest, $\theta$ being the angle between their directions (Malus's law). In stops:

$$n = 1 + \log_2 \frac{1}{\cos^2\theta}$$

At $\theta = 60^\circ$, $\cos^2\theta = 0.25$ and $n = 3$. Seven stops need $\cos^2\theta = 2^{-6}$, so $\cos\theta = 1/8$ and $\theta \approx 82.8^\circ$. Nine need $\cos\theta = 1/16$ and $\theta \approx 86.4^\circ$.

The dial grows touchy as it darkens: one degree either way gives 2.9 to 3.1 stops near three, 6.6 to 7.4 near seven and 8.3 to 9.9 near nine. On a wide lens, light crosses the filter at different angles across the frame. Oblique rays meet the two polarisers at a slightly different crossing angle, which near full strength can show as a dark cross, and blue sky, already partly polarised, darkens unevenly, which shows as a band. This is general crossed-polariser physics. Nikon says nothing about variable NDs, and filters differ. Mine spans roughly 1 to 9 stops, so at 24 mm or wider I keep it to about seven stops, short of the darkest marks, and check the corners.

06.Practical Night Work

Exposure, ISO and White Balance

A starting point for the Milky Way, only that, is the 15 s setting, which really runs 16 s (p. 669), at f/2.8 and ISO 6400 in M. With $N$ the f-number, $t$ the time in seconds and $S$ the ISO, the scene brightness at ISO 100 is

$$\text{EV}_{100} = \log_2\frac{N^2}{t} - \log_2\frac{S}{100}$$

Here $2.8^2 = 7.84$, $\log_2(7.84/16) \approx -1.03$ and $\log_2 64 = 6$, so if the exposure is right the scene is near EV −7.0, below the meter's −4 EV floor (p. 1001). With Starlight view hiding the live histogram (p. 675), judge a test frame's histogram in playback.

The Nikkor Z 24-70mm f/4 S gathers about half the light of the Tamron at f/2.8, since $(4/2.8)^2 \approx 2.04$, one stop. At 24 mm a two-pixel limit allows about 6.8 s against 10.2 s at 16 mm, another 0.58 stop. That 1.6 stops is why I take the Tamron for sharp stars and the 24-70 for trails and moonlit scenes.

Noise comes from collecting few photons, not from ISO itself, as ISO and Auto ISO explains, so aperture and time come first and ISO fills the gap. Auto ISO in M would move ISO itself (p. 145), so I turn it off.

I shoot NEF (RAW), Nikon's raw format, whose white balance can change later without loss (pp. 117-118). In camera I set Choose color temperature, range 2500 to 10,000 K, K being kelvin, the unit of colour temperature (pp. 165, 172), at about 4000 K, my starting point, so frames match. Street lamps often mix colours or cast a strong one, and under such light Nikon says Auto, Incandescent and Choose color temperature may fail and points to Preset manual (p. 176), as White Balance covers.

Focusing on Stars

Nikon rates autofocus to −10 EV, measured with an f/1.2 lens (p. 1002), and night spotlights and neon can defeat it (p. 913). So I use manual focus (MF): magnify the display on a bright star, up to about 24 times in photo mode (p. 106), and turn the ring until the star is smallest. Focus peaking, coloured outlines on sharp edges, may show nothing on points (p. 137), and the magnified view can show bright pixels and lines that need not appear in the picture (p. 915).

Save focus position at ON restores focus after a switch-off, which is how I set it for night skies, though temperature changes can still move it (p. 828), so recheck as the night cools. Focus Limiter, Saved Positions and Manual Focus covers the controls.

Star Trails With the Interval Timer

In an hour the sky turns 15.04 degrees, 0.2625 radian. At 16 mm that is $16 \times 0.2625 \approx 4.2$ mm, about 708 pixels or 12 per cent of the frame's width for an equatorial star, and about 1,061 pixels at 24 mm. One hour-long exposure would also gather an hour of heat, so trails are built from short frames stacked on a computer.

The interval timer takes them, as Silent Shooting, Timers and Time-Lapse explains, but refuses Bulb, Time and the self-timer (p. 531). My starting point is the 30 s setting, really 32 s, every 35 s, about $3600/35 \approx 103$ frames an hour. Each 3 s gap breaks a trail by $3 \times 0.197 \approx 0.59$ pixel at 16 mm and $3 \times 0.295 \approx 0.88$ pixel at 24 mm, under a pixel either way, so the dashes join.

Each exposure and its processing must fit the interval, or the camera skips one (p. 530). Long exposure NR roughly doubles the time each picture takes to record (p. 475). If that means another 32 s, as a dark frame would, it cannot fit 35 s, so I infer it must be off for the run. Nikon does not say whether the timer's Electronic shutter option, ON by default (p. 448), affects it, so check the first frames. In-camera multiple exposure cannot run with the interval timer (p. 531).

Switching off pauses the run, the battery and card can be changed meanwhile, and Restart resumes (pp. 529-530). Changing settings mid-run can end it (p. 530).

Batteries in the Cold

Cold cuts battery capacity, and the display may show a drop even when the battery is full (p. 995). Nikon rates the camera and its EN-EL15c battery for −10 to 40 °C (pp. 1009-1010), warns that a partly charged battery may fail on a cold day, and suggests keeping a spare warm, as warming can restore some charge (p. 996). It will not charge below 0 °C (p. 995).

Under the standards of CIPA, the Camera and Imaging Products Association (p. 1009), Nikon rates about 380 shots with the viewfinder alone and 410 with the monitor alone, Energy saving (photo mode) on, and lists slow shutter speeds and low temperatures among the things that cut that (p. 1016). For long exposures it recommends a full battery, a mains adapter or a portable charger (p. 148), which a later part of this guide will cover. Moving between warm and cold, keep the camera in a sealed bag until it adjusts, against condensation (p. 991).

07.Recommended Settings

Night sky. The Tamron at 16 mm and f/2.8, the 15 s setting (really 16 s) at ISO 6400 to start, focus by hand on a magnified star, and Long exposure NR on. I allow about twice the shutter time per frame.

Star trails. The Nikkor Z 24-70mm f/4 S, the interval timer at 30 s every 35 s, Long exposure NR off, a fixed white balance, a full battery and a warm spare.

Daytime water and cloud. A variable ND, A mode with Center-weighted metering at ISO 100 and Auto ISO off up to 30 s, M with d7 beyond. At 24 mm or wider, about seven stops at most.

08.Beginner Mistakes

Planning with the marked speed. The 15 s and 30 s settings run 16 s and 32 s (p. 669). Use the real figure for trails and intervals.

Leaving Silent mode on. It disables Long exposure NR (p. 846). Check the button first.

Switching off during Job NR. The picture is saved unprocessed (p. 475). Wait for the countdown.

An interval no longer than the exposure. The camera skips what it cannot fit (p. 530). Leave a few seconds spare and turn Long exposure NR off.

A variable ND at its darkest mark on a wide lens. That is where a dark cross or band can appear. Back off to about seven stops or zoom in.

A cold, half-charged battery. It may not work (p. 996). Start full and keep the spare warm.

09.Related Chapters

• Exposure Modes: mode M, shutter speed and the exposure indicators.
• Shutter Types, Rolling Shutter and Flicker: d6 and the electronic front-curtain shutter.
• Silent Shooting, Timers and Time-Lapse: the self-timer, exposure delay and interval timer arithmetic.
• Vibration Reduction: VR on a tripod.
• ISO and Auto ISO: why noise follows the light collected.
• Metering: centre-weighted metering and the histogram.
• White Balance: colour temperature and Preset manual.
• Focus Limiter, Saved Positions and Manual Focus: manual focus and Save focus position.
• Multiple Exposure, HDR Overlay and Pixel Shift: combining frames in the camera.
• Glossary: EV, stop and the other terms here.