Shaw, Joseph a. - The Digital Blue Sky at Night

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18 | OPN November 2005 www.osa-opn.org

Rayleigh-scattered moonlight creates a blue sky at night,but our eyes are not sensitive enough to perceive the color.

With the help of a digi ta l camera, however, the vivid shade of the evening sky

can come alive to anyone.

early a decade ago, I wrotean OPN article about using manual filmcameras to capture the blue color of thenight sky, which is caused by Rayleigh-scattered moonlight (November 1996,Optics & Photonics News, What Color Isthe Night Sky?, p. 54). In recent years, Ihave been asked whether digital camerascan be used for the same purpose. Myinitial experiments convinced me thatthe digital approach works well; in fact,

as I delved deeper, I learned that digitalimages require shorter exposure timesthan film.

Where does the blue go?

At visible wavelengths, moonlight issimply reflected sunlight, and the lunarreflectance is quite flat with wavelength.Although it doesnt appear so to us, aclear sky under a full moon is blue for thesame reason it is in the daytime: because

1047-6938/05/11/0018/6-$15.00 OSA

of Rayleigh scatteringthe scattering oflight by molecules in the air. (See box onp. 22, What Is Rayleigh Scattering?).

Why, then, does the night sky ap-pear black? Moonlight, which is about463,000 times weaker than sunlight, isnot bright enough to stimulate our colorvision. e human retina contains twotypes of photoreceptor cells: rods, whichare sensitive to dim light but not color,and cones, which are finely tuned for

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Te DigitalBlueSkyatNightJoseph A. Shaw


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OPN November 2005 | 19

color vision but not bright light. us,our eyes make a tradeoff between high-sensitivity black-and-white vision (withrods) and lower-sensitivity color vision(with cones).

Fortunately, a camera can do whatour eyes cannot: It can integrate thescattered light for a long enough time torecord a nighttime image of a rich bluesky that looks as if it had been takenduring the day.

Sunlight vs. moonlight

By comparing the relative brightness of

sunlight to moonlight, a photographercan approximate the exposure timerequired to capture the blue color of

the night sky. With both sunlight and

moonlight, the initial source of light isthe sun; the moon simply serves as an

intermediate reflector at night. erefore,

to estimate the difference in brightness,it is necessary to examine how the moon

reflects sunlight. All other variablesin-

cluding the solar spectrum, atmospheric

transmittance, etc.are essentially com-

mon to sunlight and moonlight.e sun-moon distance is essentially

the same as the sun-Earth distance. us,for both Earth and the moon, we can

conveniently use the same number for

the projected solid angle subtended bythe sun. A ratio of the cross-sectional area

of the sun to the square of the sun-moon

distance gives this projected solid angleas s = 6.8 10

-5 sr. Solar irradiance

(W/m2) on the Earth or the moon is

calculated by multiplying solar radiance

(W/m2 sr) by this projected solid angle.

e lunar surface reflects solar irradiancewith an approximately Lambertian reflec-

tance ofRm = 0.1 at visible wavelengths.erefore, the radiance of the full

moon can be found by multiplying the

incident solar irradiance by 0.1 anddividing by . e reflected irradiance

is converted to radiance by dividing by

, which is the projected solid angle ofthe hemisphere into which the Lam-

bertian surface scatters sunlight. e

resulting estimate is that lunar radiance

is less than solar radiance by a factor of(s/)Rm = 2.16 10-6. e Modtran

radiative transfer code yields a very simi-

lar number2.33 10-6.

Photographing theblue sky at night

To account for the weaker light of themoon, the exposure time for a photo-graph of a nighttime scene should belonger than that required for a sunlit

Digital image of the blue sky at night,

looking southeast from the east side

of Bozeman, Mont., at 9:52 p.m.

MST, November 26, 2004 (Nikon D70

camera, Nikkor 20 mm lens, ISO 200,

f/2.8, 118s). The constellation Orion

appears near the cloud at the left.

[Photos by Joseph A. Shaw]

setting by approximately 1/(2.16 10-6)

= 4.63 105. For example, if a daytime

photograph of the blue sky requires anexposure of 1/1000 s at an aperture size

of f/5.6, the nighttime blue sky should

require an exposure time of 463 s (about8 min) at the same f-number.

Achieving a properly exposed image

with this longer exposure time requiresthat the imaging system be made linear

over many orders of magnitudesome-

thing that film sometimes fails to do. is

shortcoming of filmcalled reciprocityfailuretranslates into a reduction of

sensitivity at long exposure times (also

possibly a color shift).Our calculation generates the expected

exposure times listed in the table below,

based on an exposure meter reading of1/1000 s at f/5.6 for the daytime blue

sky imaged with ISO 200 film or digital

sensitivity setting. (My film and digitalcamera meters both give the same read-

ing.) e actual value of this reference

daytime exposure varies depending on the

suns angle, atmospheric aerosol content,and so forth, but the table nevertheless

provides a good starting point.

Note that each f-number listed in

the table differs by a factor of the squareroot of two. is difference is called onestop. Each stop changes the amount

of light collected by a factor of two. e

optical power collected by an imagingsystem can be found by multiplying the

scene radiance by the system throughput,

or A product.is value is usually calculated as

the product of the entrance-pupil area

f-number Time

2.8 116 s (~ 2 min)

4 232 s (~ 4 min)

5.6 463 s (~ 8 min)

8 926 s (~ 16 min)

Theoretical exposures for a clear

blue night sky at ISO 200 based on a

daytime reading of 1/1000 s at f/5.6.[ ]


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and the image-plane projected solidanglewhich is determined as the ratioof film or detector area to the square ofthe focal length for a focus at infinity. Foran imaging system with a circular pupil,the throughput can be expressed as

AdA = ,4(f/#)2

where Adis the detector area.erefore, for a system that is linear

with detected optical power, the requiredexposure time doubles for a one-stopincrease in f-number. Similarly, theexposure time is halved for every two-foldincrease of ISO (i.e., the 116 s at f/2.8exposure becomes 58 s at f/2.8 whenthe ISO is changed from 200 to 400).

Going digital When I first tried to capture the bluenight sky with early compact digital cam-eras, the results were OK, but certainlydid not convince me to give up my filmSLR cameras. Some of the problems thatI encountered were optically slow lensesand the occurrence of the troublesomedigital noise that tends to accumulatein a charge-coupled device (CCD) orcomplementary metal oxide semicon-

ductor (CMOS) detector during longexposure times.

Astronomers have taken stunningphotographs with CCD cameras foryears, but the consumer-grade camerasthat I was using did not have cooled de-tectors or anywhere near the sensitivity of

astronomical-grade imagers. ese days,however, digital SLR cameras are avail-able that provide low enough noise andgood enough noise-reduction algorithmsto provide spectacular results. Compactdigital cameras are getting better too,although they still tend to have opticallyslow lenses and often do not provideadequate manual control.

e photo on the opening spread isone of the first pictures I took of a moon-lit scene with my Nikon D70 digital SLRcamera. I shot the photo facing southeast

toward the mountains that lie betweenBozeman, Mont., and YellowstoneNational Park at 9:52 p.m. (MountainStandard Time, MST) on November 26,2004, right at full moon.

With the moon located just above theimages field of view, the photo suffersfrom lens flare that could have been cor-rected by using a lens hood. Nevertheless,this image is a pretty good example ofthe blue sky at night. It looks just like a

daytime scene until you notice the con-stellation Orion near the cloud at the left.e streaky cloud image also providesevidence of a long exposure.

Taking this picture was easy. All I didwas set the camera on a tripod with a20-mm lens, turn on the noise-reduction

mode, and open the shutter for118 s at f/2.8 and ISO 200. (e theo-retical exposure time from the referencetable is 116 s.) I used an infrared remotecontrol to open and close the shutter withthe camera in bulb mode.

As I admired this image on thecameras LCD screen, I thought fondly ofthe many hours I had spent with my filmcamera, blindly shooting dozens of pic-tures with progressively longer exposuretimes to figure out which ones workedbest. Guided by the digital cameras LCD

screen, even a person with no photogra-phy experience could dial in the propersettings much more rapidly than I haddone with film.

One of the first things I noticed whenphotographing the night sky with digitalcameras is that the images seemed torequire shorter exposure times than thoseshot with film cameras. Entries in myphoto notebook confirmed that therewere systematic differences of up to a

Digital image of the blue sky at night,

looking north at 11:39 p.m. MDT on July

23, 2005 (Nikon D70 camera, Nikkor 20 mm

lens, ISO 400, f/2.8, 180 s). Contrast is less

than in the image on p. 18 because of extra

scattering of city lights by forest fire smoke.


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factor of two for long exposures,but there were too many variables toquantify the differences without making adirect comparison.

Digital vs. film

us, in July and August 2005, I set out

to spend several nights around the fullmoon to simultaneously photograph amoonlit scene with film and digital cam-eras. I found that the digital camera didindeed require a shorter exposure timethan film. Exposures differed by aboutone-half to one stop with several-minuteto tens-of-minute exposures.

One possible explanation is thatnear-infrared light exposes digital imagesfaster, since CCDs are much more sensi-tive at these wavelengths than normalfilm. However, if this had been a signifi-

cant factor contributing to the shorterexposures, I would have expected the im-ages to look stranger than they did, sincevegetation is unusually bright in the nearinfrared. Moreover, the detectors in thesecameras have a filter that blocks most ofthe near-infrared light.

Nevertheless, I discovered by accidentthat, in low-light conditions, my camerastill detects some of the near-infraredremote control beam. One night, I kept

noticing that blurry, UFO-looking redblobs were appearing in my Milky Wayimages until I started pointing the shutterremote control away from the lens morecarefully. (e beam cannot be seen easilyin daytime pictures.)

Although the integration of residual

near-infrared light may speed up the ex-posure a little on the digital camera, I amnot convinced that this is a major factor.Instead, it appears that film reciprocityfailure is the primary culpritmainlybecause the exposure differences seem togrow with exposure time.

e two photos above left and centerwere taken simultaneously from a digitaland film camera, respectively. e firstdigital picture (aboveleft on p. 20) is sig-nificantly brighter than the film picture,which has been scanned carefully in an

attempt to retain the original exposure.ese pictures were taken near the end ofmy film-digital comparison experimentnear midnight (Mountain Daylight Time,MDT) on July 23, 2005, two days afterfull moon. I shot these images lookingdown a narrow draw in a plateau justeast of Bozeman, facing north toward theBridger Mountains. is is the location ofa hiking trail that wraps around the eastside of my neighborhood.

For the experiment, I used a 28-mmlens on a Nikon FM2 camera loaded withslide film and a 20-mm lens on a NikonD70 digital camera to approximatelycompensate for the 1.5 smaller size ofthe CCD relative to 35-mm film. Bothpictures are 180-s exposures at f/2.8 and

ISO 400. I estimate that the film imageis at least one full stop underexposedrelative to the digital image. (e filmimage best matches the mean of digitalimages taken with 90-s and 60-s expo-sures just a few minutes earlier.) Filmreciprocity failure is the most likely cause.

Actual vs. theoretical exposures

Quantifying differences between film anddigital pictures is difficult at best: Scannedfilm images are subject to user-adjustablescanner settings, leaving it up to our eyes

to judge between slides and digital imagesdisplayed on a calibrated monitor. Mea-suring variations among digital images,on the other hand, is much easier becausedigital cameras can display histogramsgraphs that display the distribution ofbrightness levels in a scene.

As a reference for digital imagecomparisons, I used the histogram forthe daytime image shown in the figure atright, whose exposure exactly matches the

Slide film image corresponding to

image at left (Nikon FM2 camera,

Sigma 28 mm lens, same exposure).

The underexposure by at least one

stop relative to the digital image to

the left/right seems to be caused by

film reciprocity failure.

A reference daytime photograph of

the same scene, taken at 10:00 a.m.

MDT on Aug. 20, 2005 (Nikon D70

camera, Nikkor 20 mm lens, ISO

200, f/2.8, 1/4000 s).


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daytime in the reference table on p. 19(Aug. 20, 2005, 10:00 a.m. MDT, ISO200, f/2.8, 1/4000 s). e histogram forthis picture revealed a fairly uniform dis-tribution of pixels, with digital numbersmostly between 100 and 200 (the fullrange of 8-bit images is 0-255).

Using the daytime reference imagemakes it possible to sort through a set ofdigital images with different exposuresto find the one that best approximates

daytime, thereby comparing actual andtheoretical night-sky exposures. isprocess led to the selection of the imageshown on p. 20 (left) as the best day-like exposure from that night. However,the exposure of 180 s at f/2.8 and ISO400 is about three times longer than thetheoretical value of 58 s from the tableon p. 19 (for f/2.8 and ISO 400). Whataccounts for the discrepancy?

e photo atright (p. 23) shows

the same scene as theprevious three photo-

graphs (on pp. 20-1),but is in a vertical format

and was taken with a longerexposure time. It was shot on

August 21, 2005, at 1:33 a.m. MDTat ISO 200, f/5.6. Exposure time is963 s (16 min)about twice the theo-retical value from the reference table.

e picture was taken one nightafter a full moon, and thus the lunaropposition effect may contribute slightly

to the longer exposure, as does the lowermoon angle. Vertical images also requirelonger exposures because of the extratime it takes to achieve day-like imaginghigh in the sky versus at the horizon.In this longer exposure, star streaks beginto form circular paths around Polaristhe North Star.

Which approach is better?

Both digital cameras and film camerashave advantages and drawbacks. Digitalcameras offer many features that make

this kind of photography easier and moreenjoyable than film. I love the instantfeedback that my digital camera providesas well as its excellent technical capabili-ties. However, working with my old filmcamera reminded me how much I love itsfeel and its incredibly large and brightviewfinder. I hope that future digital SLRcameras will have viewfinders as good asthe one on my old FM2.

My film camera also operates withouta battery, which is an enormous advan-tage in cold weather. Nevertheless, the

rechargeable batteries used in digitalcameras have a long life, and I alwayskeep a charged spare with me. Anothersignificant advantage of digital camerasis that you do not have to take as manynotes, because each digital image is storedwith complete data about the camera andlens settings.

One thing I dislike about my digitalcamera, however, is that the noise-

[ What Is Rayleigh Scattering? ]

In 1871, John W. Strutt, the third

Baron Rayleigh (usually referred to

simply as Lord Rayleigh), showed

that the scattering of light by small

particles varies as the inverse fourth

power of wavelength (1/4). Due to

this inverse dependence on wave-

length, air molecules in the Earths

atmosphere scatter about 4-5 times

more short-wavelength blue light

than longer-wavelength red light.

In 1899, Rayleigh identified atmo-

spheric molecules as a sufficientsource of scattering to explain the

blue sky.

Rayleigh scattering theory ap-

plies to dipoles. In other words, it is

independent of particle shape and

relevant only to particles that are

much smaller than the wavelength

of light, such as atmospheric gas

molecules. Much larger aerosols

and dust particles require a higher-

order theory, such as Mie scattering,

which is applicable to spheres.

First off, the differ-ence is not as dramatic

as it might initially ap-pear. ats because theexposure time must bechanged by a factor of two toaccomplish significantly differentphotographic exposures. Still, there issomething very interesting causing thispicture to require such a long exposurecompared with the theoretical value.

By taking pictures on several nightsduring August 2005, I confirmed thatthose taken exactly at full moon (e.g.,Aug. 19) are consistently one-quarter to

one-half stop brighter than those takenwith identical exposures two nights fol-lowing a full moon (e.g., Aug. 21). ecause is apparently the strong retro-reflec-tive character of the lunar surface (thelunar opposition effect).

In reality, moonlight is much brighterat full moon than would be expectedfrom considering the illuminated area atfull moon relative to just before or after.However, the Lambertian assumptionthat we made for the lunar surface doesnot take this into account. To verify the

significance of this effect, I found a com-parable histogram from an image on Aug.19, 2005, right at full moon, which had a92-s exposure at f/2.8 and ISO 400 (halfthe exposure time of thephoto on p. 20).

Another potentially significant factor,which I ignored when calculating thetheoretical moonlight exposure, is thedifferent zenith angle of the moon andsun. e moon is lower in the sky duringsummer in the northern hemispherethan it is during winter, while the sum-mer sun is higher. Although the earlier

calculation assumed that the effect of theatmosphere was the same for sunlight andmoonlight, this difference in zenith anglecould increase the required summertimenight-sky exposures by about one-quarterto possibly one-half stop. us, it appearsthat the combination of the lunar opposi-tion effect and the greater atmosphericextinction for a lower moon in summeraccounts for my observations.


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Vertical nighttime photograph taken at

01:33 a.m., Aug. 21, 2005 (Nikon D70

camera, Nikkor 20 mm lens,

ISO 200, f/5.6, 963 s).

[ References and Resources ]

>> J.N. Howard, John William Strutt, thirdBaron Rayleigh, Appl. Opt. 3, 1091-101(1964).

>> R. Greenler, Rainbows, Halos, and Glories,Cambridge, U.K.: Cambridge Univ. Press(1980).

>> C.F. Bohren and D.R. Huffman, Absorptionand scattering of light by small particles,New York: John Wiley and Sons (1983).

>> J.A. Shaw, What color is the night sky?,Optics & Photonics News 7 (11), 54-5(1996).

>> J.A. Shaw, Modeling infrared lunar radi-ance, Opt. Eng. 38 (10), 1763-4 (1999).

reduction algorithm requires processingtime equal to the exposure time. For a

1-min exposure, this is not so bad, butwaiting 20 min for a 10-min exposurecan be really annoying. Some camerashave faster noise-reduction processing,and I hope that most others will soon beimproved in this regard.

is kind of photography can be quiteuseful for measuring clouds and haze atnight, as well as for teaching radiometryand optical detection. Not to mentionhow fun it is to view something in aphotograph that your own eyes cannotsee. To capture the digital blue sky at

night for yourself, youll need a camerawith fully manual capability that includesa bulb setting, a tripod and, of course, afull moon. Good luck!

Acknowledgments

My digital exploration of the nightsky has been encouraged by questionsfrom Prof. C.F. Bohren (Penn State)and numerous slide-show attendees andstudents, and by discussions with myfather, Prof. G.E. Shaw (University ofAlaska). I originally got the idea of

photographing the blue sky at nightfrom Robert Greenlers book, Rainbows,Halos, and Glories.

[Joseph Shaw ([email protected]) isan associate professor in the department of

electrical and computer engineering atMontana State University in Bozeman. ]Member

Shaw, Joseph a. - The Digital Blue Sky at Night

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