Minimum Shutter Speed – Revised!
By Doug Criner
For a handheld 35mm camera, the conventional rule of thumb is to select a shutter speed of at least the reciprocal of the lens’ focal length to avoid blurring due to camera shake. For example, with a "normal" 50mm lens, the shutter speed should be no slower than 1/50th of a second.
The basis of this rule of thumb is seldom discussed, inviting the question whether it is, in fact, correct. I have conducted experiments that indicate that although the reciprocal-of-focal-length rule may be adequate for small enlargements, sharpness can be increased with significantly faster shutter speeds. Indeed, buried within one of Ansel Adams' books, he suggests that with a normal lens and a handheld camera, a shutter speed of anything less than 1/250th second may produce less than a completely sharp image. (See The Camera, Little, Brown and Company, 1980, p. 116.)
How steady is steady?
Just how steady can a camera be held? To answer this question, I used an enlarger alignment device which is essentially a laser mounted in a box about the size and weight of a 35mm camera. From 30 feet, trying my best, the laser spot would dance around within about a 1.5-inch circle on the wall. Using trigonometry, this corresponds to jittering within a solid angle of about 0.24˚. (You might try the same experiment with a laser pointer securely taped to a camera.)
The next question is how rapidly the laser spot moved within the circle. Without sophisticated instrumentation, I chose to use published medical data for the frequency of normal human nervous system tremor. The normal frequency range is 4-12 Hz. I assumed that my tremor rate was in the middle of that range, 8 Hz. In half a cycle, 1/16th second, a handheld camera may be expected to swing through 0.24˚, which translates to an average tremor of 0.24 x 16 =3.8˚/sec.
Film resolving power
How can we relate this jitter of 3.8˚/sec to the effect on image sharpness? Image sharpness is limited by the film’s resolving power, which for Kodak Tri-X is 100 lines per mm. If the image projected onto the film during exposure moves less than, say, half of a line spacing, we’ve probably achieved the film's maximum sharpness.
With resolving power of 100 lines per mm, half the line spacing is 0.005 mm. For a 35mm camera with a 50mm lens, the angle of view is about 45˚ and the dimension of the film is, duh, 35 mm. With a little math, jiggling the camera 3.8˚/sec is seen to correspond to 3.1 mm/sec (so a 1-sec exposure would be hopelessly blurred–which even a beginning photographer well knows). To limit image movement during exposure to 0.005 mm, one-half the film's resolving power, the exposure time should be 0.005 / 3.1 = 0.0016 sec. This would call for a shutter speed slightly faster than 1/500th second (compared to the rule-of-thumb speed of 1/50th sec).
Clearly, the conventional rule of thumb does not come close the achieving maximum image sharpness. It only works because the resultant blurring due to camera shake may not be noticeable for small enlargements.
Conclusion
I propose a revised rule of thumb: use at least twice the shutter speed called for under the old rule. For example, using a "normal" 50mm lens, use, say, 1/125th second rather than 1/60th second. Even better results can be achieved by using up to ten times the old rule’s shutter speed, i.e., 1/500th second in the example given.
Question: What About a Digital Camera?
Roy
Thomas at Black Dog Photography, Hoboken, NJ, wrote: "I just read
your thesis on focal length and camera shake and shutter speed. Very
impressive. I believe Ansel Adams used 1/250 second as a minimum because
he shot in large format, usually with a 300mm lens hence the equation. I
have read the book but don't recall the paragraph.
My question is: If minimum shutter speed is somehow related to focal
length and film size, then do the minimum numbers drop in the digital
world? Restated: Camera shake is exacerbated by film size. Medium format
is more sensitive to shake than 35mm so the minimum shutter speed would be
1/125. And of course large format needs even faster speeds. Since
digital sensors are relatively small does the shutter speed relationship
also follow? A "normal" (50mm in 35mm world) is about 14mm in
the digital
world. So.... would 1/14 second be true to the OLD rule of reciprocal of
focal length?"
Answer: Roy is on the right track, but before getting into the purely digital aspects of your question, let’s assume that his camera with the 14mm lens is a film camera, not digital. Then, the “old” rule of thumb would recommend a minimum shutter speed of 1/14 second. (Under my revised rule, I would make it one or two stops faster, 1/30 or 1/60 second.) In general, the “old” recommended speed is the reciprocal of the lens focal length, no matter what the size of the film—so it would be the same drill whether for a 35mm camera or a medium format camera.
Now, the size of the film affects the angle of view for a given focal length. For example, we know that a “normal” lens (one that has about a 45º angle of view, roughly the same as human vision) for a 35mm camera is a 50mm lens. For my medium format camera, with a film dimension of 60mm, the "normal" lens is about 85mm (50mm x 35/60 = 85.7mm), and the minimum shutter speed per the “old” rule is 1/85 second, say 1/125; make it one or two stops faster for my rule, and it’s 1/250 or 1/500 second.
Implicit in all of this is that the “resolving power” (lines per mm) of film is the same no matter what camera it’s in or the size of the film. The minimum shutter speed is proportional to the film size and the film’s resolving power, and is inversely proportional to the field of view of the lens (degrees). The lens' focal length is “in there” somewhere, because the field of view (degrees), lens focal length, and the film size are all interrelated.
For my
film camera study, I assumed the resolving power of Tri-X film, which is
listed by Kodak at 100 lines/mm. If we were to use a film with lower
resolving power, then the minimum shutter speed would actually be slower.
Therefore, before we can answer your question, we must estimate the
resolving power of the digital imaging system inside your digital camera
and the size of the camera’s pixel sensor array.
Resolving Power of Digital Cameras
Roy
reports that for his particular digital camera a 14mm focal length is
“normal.” Since we know that a 50mm lens is “normal” for a 35mm camera,
the size of the array of pixel sensors (the equivalent “film size”) within
his digital camera must be about 35mm x (14/50) = 9.8 ≈ 10mm (less than a
third the size of 35mm film). (For simplicity, I’m using the width of the
image, the long dimension; it would be more accurate to use the diagonal
dimension of a 35mm frame.) This gives us one of our “unknowns,” and we
now must estimate the resolving power (lines/mm) of Roy’s digital camera.
Roy didn’t specify his camera’s number of pixels, but let’s say that it
has 4.0 megapixels. Then the spacing of the pixels is about: √[(10mm x
10mm) / (4.0 x 106 pixels)] = 0.005mm. I’m ignoring
two fine points: 1) the sensor array is likely rectangular, not square,
and 2) the spacing between parallel rows of pixel sensors will be larger,
by a factor of √2, in a diagonal direction across the array.
With
this pixel spacing of 0.005mm, we couldn't expect to resolve lines with
the same spacing. Probably, we could expect to begin resolving lines with
twice that spacing, 0.01mm (i.e., two pixels for each line). The
equivalent resolution is: 1/0.01 = 100 lines/mm (coincidentally, the same
resolving power as Tri-X film).
To adapt the old inverse-of-focal-length rule to this digital
camera at “normal” focal length, we need to multiply the “old rule” of
1/14 second by the ratios of image resolution. Thus, the “old rule”
minimum shutter speed for the digital camera with a “normal” lens = (1/14
sec) x (100 lines/100 lines) = 1/14 sec ≈ 1/15 second.
Roy’s “old rule” answer of 1/14 second is correct, but serendipitously so. That speed is only correct for my assumption of a 4 megapixel camera. If it were 2 megapixel or 8 megapixel, with the same 10 mm sensor array size, his answer would have been off by a factor of √2 ≈ 1.4.
Interpreting Digital Camera Specs
Out of curiosity, I checked the specs for my Kodak DX6440 digital camera, a 4-megapixel “point and shoot” model with a zoom lens. Here is selected information published in the user’s manual
•Image Sensor: 1/1.25 inch charge coupled device (CCD), 4:3 aspect ratio
•Lens focal length: variable, 33–132
•Slowest shutter speed, @ wide lens, Auto Mode: 1/60 sec
•Normal lens focal length: not given
CCD image sensor arrays are sized in an arcane manner, a legacy from early television days (for more details, refer to the website referenced below). But suffice it to say, the long dimension of a 1/1.25 inch array is about 5.6mm. We may now compute the “normal” lens focal length, by factoring the known “normal” lens size of 50mm for a 35mm camera: 50mm x 5.6/35 = 8mm. But wait, this “normal” focal length doesn’t even fall within the zoom lens’ supposed range, 33–132mm. What gives?
Engraved on the lens itself is this data: “33mm–132mm (Equiv).” The manufacturer has listed the focal length range using the “equivalent” focal lengths for a 35mm camera. Therefore, the equivalent “normal” focal length of 50mm corresponds to a true focal length of 8mm, and the lens’ real range of focal lengths varies from 5.3mm to 21mm.
The spacing of the pixel sensors in this CCD chip is about: √[(5.6mm x 5.6mm)/(4 x 106 pixels)] = 0.0028mm. As explained above, we might expect to resolve lines with twice that spacing: 0.0028mm x 2 = 0.0056mm. This corresponds to a resolving power of 1/0.0056 = 179 lines/mm (nearly double Tri-X film’s resolving power, 100 lines/mm).
We may now compute the minimum shutter speed to achieve maximum image sharpness. At the “normal” focal length of 8mm, the minimum shutter speed, using the “old” rule is: (1/8 sec) x (100 lines/179 lines) = 0.070 sec ≈ 1/15 sec. Per my revised rule of thumb, increase this speed by one or two stops, so select 1/30–1/60 second as the minimum shutter speed. Indeed, the Kodak specifications for this camera, when in the Auto Mode, calls for a minimum shutter speed of 1/60 second at wide angle. With my “new” rule of thumb for selecting minimum shutter speed, I have seemingly rediscovered what Ansel Adams and even Kodak have known all along.
What Ansel Adams Said
Since Roy was intrigued by my citation of Ansel Adams’ findings, I went back to Ansel’s book, The Camera, page 116, which states:
Tests I conducted some years ago, photographing leafless trees against the sky, indicated that, using a normal lens with a hand-held camera, the slowest shutter speed that ensured maximum sharpness was 1/250 second. I found that even with firm body support image sharpness was noticeably degraded at 1/125 second, a speed that many photographers consider safe for hand-holding a camera with normal lens.
I’m quite sure, based on the context of Ansel’s statement, that he conducted his experiment with a 35mm camera, and that his recommended minimum shutter speed of 1/250 applies to a 35mm camera with a 50mm (normal) lens. What is the equivalent speed of for a medium format with film dimension of, say, 60mm, also equipped with a normal lens? It is: (1/250 sec) x (35mm/60mm) = 0.00233 ≈ 1/500 sec, or twice as fast as for the 35mm camera.
In general, the equivalent shutter speeds between two different camera/film systems is inversely proportional to the ratio of the lens’ focal lengths. Therefore, if 1/25 second is the desired shutter speed for Camera A with a 30mm lens, the equivalent shutter speed for Camera B, also with a 30mm lens, is 1/25 second—irrespective of the relative film sizes of the two cameras. This is true in general, assuming the films have the same resolving power.
Similarly, if two film cameras, A and B, taking different film sizes, each have lenses with the same angle of vision, but of course with different focal lengths (F), the equivalent shutter speed (S) is given by: SA = SB x (FA/FB).
My studies merely corroborate those of Ansel, but Ansel’s conclusions regarding shutter speed seemingly never achieved widespread notice; adherence to the “old” reciprocal-of-focal-length rule continues to this day. Perhaps with the Internet available to disseminate these findings, the “new” rule will gain greater acceptance.
References
This website provides information on the somewhat arcane sizing conventions used for CCD sensor chips:
http://www.dpreview.com/news/0210/02100402sensorsizes.asp
® Doug Criner, 2004