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镜头焦距与视野计算器  

2015-09-06 16:19:26|  分类: 专业 |  标签: |举报 |字号 订阅

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Computes Field of View of camera and lens, both the dimensional size of the Field Of View seen at a specified distance, and also Angle Of View, for any sensor size.

Many other Field of View calculators assume 3:2 DSLR sensors only, but this one also offers 4:3 and compacts, and 16:9 movies too. Or, entering the sensor size can be any ratio.

Accuracy is best if you can enter the actual sensor dimensions (mm, from camera manual specifications) - Option 1.

Or, if you can determine the crop factor, sensor size can be computed - Option 3, see crop factor notes below.

Or, you may be able to select one of the general sensor descriptions (or film size) - Option 4. Film should be good, but the inch sensor numbers may be less accurate.

Or, if you can measure the field of view at a specified distance, and know the focal length, sensor size can be calculated - Option 8.

One example: Suppose you want a portrait to include a 2x3 foot subject area. You know you need to stand back six or eight feet for proper portrait perspective. What focal length is that field size going to require? And the background may be five feet further back, how large does it have to be? This calculator can plan or verify your choice. If you want to see fractions of inches better, you can enter distance as inches (ten feet = 120 inches), but realistically, the accuracy (of the focal length) may not be up to fractions of an inch, not at close distances (see Macrobelow).

Enter Focal Length and Distance, select an Option 1-7, then click Compute. FOV depends on focal length, distance, and sensor size.

Computing Angle of View (degrees) for a lens focal length and sensor is independent of subject distance, so for that goal, just ignore the Dimension part.

Field of View CalculatorField DimensionAngle of View
Lens Focal Length (mm)Horizontal DimensionHorizontal Degrees
Subject DistanceVertical DimensionVertical Degrees
Any units for Distance - feet or meters, inches or cubits. Dimension results are in the same units.Diagonal DimensionDiagonal Degrees

Options

1Sensor size Horizontal mmSensor size
Vertical mm

2

Sensor Width Horizontal mmAspect Ratio, Width: Height 3:2 (DSLR) 4:3 compact, phone 16:9 HD camcorder 

3

Crop factor (multiplier)Aspect Ratio, Width: Height 3:2 (DSLR) 4:3 compact, phone 16:9 in 3:2 camera 16:9 HD in 4:3 cam 16:9 HD camcorder 

4

Sensor Size Description 1/10" CCD 1/8" CCD 1/6" CCD 1/4" CCD 1/3.2" iPhone 5 1/3" iPhone 5S & 6 1/2.7" CCD 1/2.5" CCD 1/2.3" CCD 1/2" CCD 1/1.8" CCD 1/1.7" CCD 1/1.6" CCD 2/3" Fuji, Nokia 1/1.2" CCD 1" CCD 4/3 Olympus, Panasonic CX - Nikon 1, Sony Foveon Sigma APS-H 1.3x crop, Canon APS-C 1.6x crop, Canon APS-C 1.5x crop Nikon FX 1.2x crop Nikon FX 5:4 crop DSLR full frame, 1x crop Kodak Disk film Minox film 110 film 126 film 127 film 40x40mm 127 film 60x40mm 828 film 8 mm film Super 8 mm film 16 mm film Super 16 mm film APS Classic film APS Group/HDTV film APS Panoramic film 35mm movie film Super 35mm movie film 18x24 mm half-frame 35 mm 35mm film XPAN film 6 x 4.5 cm 120 film 6 x 6 cm 120 film 6 x 7 cm 120 film 6 x 9 cm 120 film 4 x 5 inch film 5 x 7 inch film 8 x 10 inch film 

Mostly this is Film Size. The 1/x inch numbers are a vague way to NOT tell how tiny the little CCD sensor is.

5

For subject distance specified above,And Sensor Size Option Above

1 2 3 4

To find Focal Length giving a Field of View of

Dimension units in the

Horizontal

Vertical

Diagonal

Direction

6

For subject distance specified above,To find Focal Length giving a Field of View of

angular Degrees in

7

For the Focal Length specified above,To find Subject Distance giving a Field of View of

Dimension units in the

8

For the measured Field Horizontal and Vertical Dimensions you enter at top above, measured AT the Focal Length and Distance entered, compute the Sensor Size (the distance should be at least six feet, 8 or 10 is better)

Numbers only  (a NaN result will mean an input is Not A Number). Decimal points are OK.


Crop factor is the ratio of (Equivalent focal length for 35mm film seeing the same view) divided by the actual focal length on this camera's sensor size. For example, the specification for a compact camera might say:
    "Focal Length: 4.5 (W) - 81.0 (T) mm (35mm film equivalent: 25-450mm)".   (the wide angle and telephoto extents) 
That case makes crop factor be 25mm/4.5mm or 450mm/81mm, both equal to 5.55 crop factor. However, focal length of compacts is probably not known except at the extremes that the spec mentions. Crop factor is often specified as a slightly rounded number. For example, the 35mm film frame is 36 mm wide, and if the DX sensor is 23.5 mm width, then it is actually 36mm/23.5mm = 1.53 crop. But, the focal length number is also approximated anyway.

Entering exact sensor dimensions above would be the most precise. The camera manufacturers specify the equivalent 35mm crop factor from the diagonal ratio to 35mm film (because many of us are very familiar with 35mm film, and crop factor tells us what to expect now). We may not know sensor size or focal length on compacts, except at either end of the zoom range, but then we can determine crop factor, for example, if they specify their 6.1mm lens is equivalent of 24mm lens on a 35mm camera, then obviously their crop factor is 24/6.1 = 3.93.

The differences in the Aspect menu in Option 3 above is that DSLR and compacts take 3:2 or 4:3 photos, larger than 1920x1080, and their 16:9 movies are constrained within that sensor size, fitting its width. Whereas camcorders typically take 16:9 still photos that are still 1920x1080, with movies fitting the full diagonal, not constrained by any 3:2 or 4:3 sensor width.

Typically photo cameras will use the full sensor width for their HD movie width (D7100, D600, D750) and that is assumed here, but for example, the Nikon D800/D810 use slightly less width (these D8xx manuals specify the sensor image area for HD movies is 32.8 x 18.4 FX, and 23.4 x 13.2 DX).

There are approximations. The math is precise, but the data is slightly less so. However, the results certainly are close enough to be very useful in any practical case. My experience is that the field is fairly accurate (at distances 1 meter or more), assuming you actually know your parameters. Some problems are:

The Marked focal length of any lens is a rounded nominal number, like 50 or 60 mm. The actual can be a few percent different. Furthermore, the Marked focal length is only applicable to focus at infinity. Focal length necessarily increases when lens is extended forward to focus closer. Also zoom lenses can do other internal tricks with actual focal length (some zooms can be shorter when up close, instead of longer). Focal length will be less accurate at very close distances, and field of view becomes a little smaller, but any error should be small if focused beyond one meter. You also have to measure your distance and field dimensions accurately too. And of course, we are only seeking a ballpark number anyway, we adjust small differences with our subject framing.

Actual focal length can be determined by the magnification (Wikipedia). Or, the focal length (f), the distance from the front nodal point to the object to photograph (s1), and the distance from the rear nodal point to the image plane (s2) are related by this equation:

If OK with a little geometry and algebra, you can see the derivation of this classic Thin Lens Equation at the Khan Academy.

In this equation, we can see if the subject at s1 is at infinity, then 1/s1 is zero, so then s2 = f. The marked focal length applies when focused at infinity.

fov

The field of view math is basic trigonometry. The focal length measures from lens node to sensor. We compute the right triangle on center line, of half the sensor dimension, so the half lens angle = arctan (sensor dimension / (2 * focal length)). The Subject distance is in front of lens node, with same opposite angle. Field dimension = 2 * distance * tan (center line half angle). The problem is that focal length f becomes longer when focused at close distances (but the opposite can be true of a few zoom lenses). That becomes an insignificant field of view difference at normal distances, 1 meter or more.

Multi-element camera lenses are "thick" and more complex. We are not told where the nodes are designed, normally inside the lens somewhere, but some are outside. For telephoto lenses, the rear node (focal length from sensor plane) is in front of the front lens surface. The designer's term telephoto is about the reposition of the nodal point so that the physical lens is NOT longer than its focal length. Yet, this rear node is generally behind the rear lens surface of a wide angle lens (lens moved well forward to provide room to allow the larger SLR mirror to rise... 12mm lens, 24mm mirror, etc). This nodal difference is only a few inches, but it affects where the focal length is measured. And it shifts a bit as the lens is focused closer. Repeating, the focal length marked on the lens is specified for focus at infinity.

The Subject distance S is measured to the sensor focal plane (it is the "focus distance"), where we see a symbol like Φ marked on the top of the camera (near rear of top LCD). The line across the circle indicates the location of the sensor plane (for focus measurements). However, the Thin Lens Equation uses the distance d in front of lens. This is why we often see in equations: (S - f) used for d.

For Macro, computing magnification is more convenient than focal length (since we don't really know focal length at macro extension). Focal length and subject distance determine Magnification, which is the ratio of size of image to size of actual subject. Or size of sensor to the size of the remote field. We could compute that here, but magnification has more significance up closer (easier for macro), which is where our knowledge of the actual focal length is weakest. We could measure the field to compute the actual magnification, to then know the actual focal length. However Magnification is simply:
    m = s2/s1.   Or m = f/d.   Or m = f/(S-f).

So from this, we know macro field of view is simply the sensor dimensions, divided by the magnification. Let's say it this way:

1:1 macro (magnification 1), the field of view is exactly the same size as the sensor. 
1:2 macro (0.5 magnification), the field of view is twice the size of the sensor. 
1:4 macro (0.25 magnification), the field of view is four times the size of the sensor.

This is true of any focal length for any lens (or method) that can achieve the magnification. Focal length and subject distance are obviously the factors determining magnification (it is still about them), but magnification ratio is simply easier work for macro.

The easiest method to determine field of view for macro is to simply put a mm ruler in the field. If a 24mm sensor width sees 32 mm of ruler, then that is the field of view, and the magnification is 24/32 = 0.75 (this scale of magnification is 1 at 1:1, and is 0 at infinity).

The definition of macro 1:1 magnification is that the focal length and subject distance are equal (distances in front of and behind the lens nodes are necessarily equal, creating 1:1 magnification). In this Thin Lens Equation, if s1 and s2 are equal, the formula is then 2/s1 = 1/f, or 2f = s1. So lens extension to 2f gives 1:1. And since f/stop number = f / diameter, then if 2f, then f/stop number is 2x too, which a double f/stop number is 2 stops change, which is the aperture loss at 1:1. We know those things, this is just why.

But the point here, if f is actually 2f at 1:1 macro, the field of view changes with it. None of the FOV calculators are for macro situations (too close, magnification is instead the rule there). Field of View calculators expect subject distance to be at least a meter or two, reducing the focal length error to be insignificant.


http://www.scantips.com/lights/fieldofview.html

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