# A few scanning tips

## Extension Tube Basic Formulas (for macro photography)

Macro lenses are expensive, but are very popular, because they are extremely convenient to use. They focus easily, just like any lens at any supported magnification from infinity to closest macro range, which is often 1:1 at closest focus. It’s a good bet that a macro lens will become a favorite lens.

Extension tubes are considerably more difficult to use, focusing at only one distance, needing formulas and calculators to help predict that setup. And extension tubes generally require focusing by changing the physical distance between subject and camera, but they are less expensive.

The previous page has a Calculator to copy slides that calculates this.

One commonly used formula for magnification is m = object size on sensor / real life object size. This magnification number normally does not exceed 1x (the subject image is smaller on the camera sensor than in real life). This formula is the definition of magnification computing for cameras.

That formula and the next one come from the similar triangles in the geometry here, size is proportional to distance from lens.

So another formula is m = focal length / focus distance. This works well enough for normal photography distances, but it fails badly for macro work. Because we don’t know actual modified focal length in most macro cases, and focal length and subject distance are measured to internal nodes somewhere inside the complex camera lens (and which move), and which we don’t know. There are formulas for it, but users don’t know where to measure the distances to. At small macro distances, these node locations might be significantly different than we might guess. So the first fact about macro is that calculations are instead based on magnification instead of distances, because we can measure that in the actual result.

Internal extension: Focusing closer increases lens focal length. In older lenses, we see the front lens element move forward at closer focus. Many more modern lenses use internal focus, moving unseen internal elements forward. There can be a few minor ifs and buts, but generally, the focal length increases a bit when focused closer. The focal length marked on the lens applies only at Infinity focus, otherwise closer extends it. Internal extension is how much it moves forward, which is the maximum focal length increase at closest distance. Any added extension tube behind the lens is an external extension of focal length.

Magnification: Macro computing is about magnification. Magnification is the Size of subject image / Size of the real life subject (is normally small, less than 1x). For a slide copy to match the sensors size, the “subject” is the slide, in which case this could be Magnification = Height of Sensor / Height of Slide. Or, same idea for the Widths, which can be different due to differences of Aspect Ratio, so the correct number to use is whichever is the smallest magnification number (both dimensions have to fit). A 1:1 copy is 1x magnification, and a half size copy is 0.5x magnification.

Maximum Magnification at Closest Focus: Focusing closer increases magnification, because the closer subject appears larger, and the focal length is also generally increased. Macro work is all about magnification. Specifications of regular lenses normally specify the Maximum Magnification at its Closest Focus distance, which is generally limited to the 0.1x to 0.2x range for regular lenses, like perhaps 0.15x for a 50 mm lens at a foot or two of distance. The 0.15x means the image of the object on the sensor is 15% of real life size (is normally a reduced size instead of an enlargement, but closer distance and longer focal length increases it.). If you don’t know your lens specification for Magnification at Closest Focus, the B&H product pages probably show it for lenses still in production. Otherwise, you can measure it, below at Determining the Known Lens Magnification.

Here, my terms will call Maximum Magnification at Closest Focus to be Closest_mag. And Focal_length is the Focal Length marked on the lens which applies when focused at Infinity, and Exten_length is the added Extension Tube length.

## Extension Tube Formulas

1. The (minimum) magnification with lens focus set to Infinity is

Magnification = Exten_length / Focal_length

Basically this says when focal length and extension tube are numerically equal (and lens focus is at Infinity), we get 1x magnification, which is 1:1 (image size is same as real life size). That relation is necessarily implied by the diagram above.

2. The (maximum) Magnification at Closest Focus is

Magnification =
Exten_length + (Focal_length x Closest_Mag)
Focal_length

(Closest_mag is normally specified in the modern lens specification, meaning with no extension tube then)

3. The additional internal focus extension at Closest Focus is

internal extension = Focal_length x Closest_Mag

(50mm FL and 0.15x at Closest Focus is 7.5 mm internal extension. Formula 2 simply adds it as Total Extension)

To copy slides, dividing the size of the slide image seen by the size of the camera senor (both being the full size dimension) computes the magnification needed. Then the goal of the camera lens setup is to provide that magnification.

If your extension tube setup has too much magnification to see all of your slide area, then you need a shorter extension tube, and/or a longer focal length lens. But if it is not very far wrong, you might first try focusing the lens towards its infinity setting to possibly reduce magnification enough. The calculator on the previous page tries to inform you of these situations when that can work. Or to use the calculator with the lens focused instead at Infinity, you must specify the Maximum Magnification at Closest Focus to be zero (due to the missing internal focus extension when at Infinity).

### Calculator Lens Option 2 (extension tube) examples

This chart shows the elementary basics of extension tubes. The calculator will compute these same expected relationships. The first case is just the definition of the lens spec for Closest_Mag.

 Case # 1 2 3 4 5 Focal Length 50 mm 50 mm 50 mm 50 mm 50 mm Focus at Closest Closest Infinity Infinity Infinity Mag at Closest 0.15x 0.15x 0 0 0 Internal extension 7.5 mm 7.5 mm 0 0 0 Extension tube 0 42.5 mm 7.5 mm 50 mm 0 Magnification 0.15x 1x 0.15x 1x 0

The calculator’s initial default spec of 50mm FL and 0.15x magnification at closest focus computes (50 x 0.15) = 7.5 mm internal focus extension (formula 3). But focusing the lens at Infinity eliminates the internal focusing extension, in which case then specifying Closest Magnification as 0 also ignores it and computes the Infinity case.

• Case 1 illustrates the lens specification, and formula 2 necessarily computes the same 0.15x mag. Computing is the purpose of the spec.
• Case 2 adds 42.5 mm of extension tube (so total extension is 42.5 + 7.5 = 50 mm, equal to the 50 mm focal length), and formula 2 computes the expected 1x mag. Formula 1 does also, if Total extension is specified.
• Case 3 focuses at the Infinity setting (indicated by specifying 0x Closest mag) and adds the missing 7.5 mm internal extension instead as an extension tube (equal to the missing internal extension computed from lens spec). Formula 2 computes the expected 0.15x mag. Specifying 0x Closest mag ignores the internal extension (if focused at Infinity) and this case uses same 7.5 mm as if an extension tube, and gets the same result.
• Case 4 focuses at the Infinity setting (and specifies 0x Closest mag) and adds 50 mm extension tube (equal to the focal length). Formulas 1 and 2 computes the expected 1x mag.
• Case 5 focuses at the Infinity setting (and specifies 0x Closest mag) and computes the expected 0x mag.

About specifying Maximum Magnification at Closest Focus to be 0 to indicate focus set at Infinity: The only actual action from that zero is to compute the internal extension to be zero (which it is if lens is set to the Infinity setting), and the rest reasonably follows. And if the internal extension is 0, the formula implies that either focal length or Maximum Magnification at Closest Focus is zero. But it’s not focal length, and Magnification at actual Infinity is necessarily zero, and we can even say that Infinity is in fact the closest focus when focused there. For example, stars at night are astronomically huge, but they are reasonably near infinity, and stars are seen as point sources here on Earth, which is defined as zero diameter. One mile (1.61 km) distance would be 0.0000311x mag (very small), but Infinity computes 0x magnification (even if our pixel size or film grain size does not have sufficient resolution to show zero size). But at Infinity lens setting, the very short 50 mm macro distance (and 50 mm total Focal Length) would be 1x, or 1:1 actual size on the sensor.

So we hear frequent statements that the added extension must equal the focal length for 1:1 reproduction (1x). But there is a little more to it, because that refers to the Total Extension. Their lens must still be focused at infinity (when the internal focus extension is zero). But if focus is set to the closest end (IMO, that’s normal practice with extension tubes, for greater magnification), the math also needs to know of the native internal extension, which is in the lens specifications indirectly, as above.

The increased exposure requirement (Exposure Factor) is (m + 1)². And that light loss is EV = log2 of this Exposure Factor. And log2(value) is log10(value) / log10(2).
Example: For magnification 0.67, Exposure increases (0.67 + 1)², = 2.79x, and that EV change is log2(2.79) = +1.48 EV.

## Determining the Known Lens magnification

The calculator computes the actual magnification of your setup, but possibly useful for extension tubes, it can also work from a Known magnification. So How to determine a Known magnification?

The wording is kinda tricky, but the concept is easy. The image frame size varies with sensor size, but:

• Camera magnification is about the lens magnification producing object magnification, and is NOT about sensor size (which is just a cropped outer frame around the edges).
• Magnification in photography is the size of an object on the sensor / divided by the real life size of the object. This was more obvious in the days of film, we could develop the film and simply measure the object size on film. Size is more indirect on digital, and we can only view it when enlarged for viewing. The same lens still makes the same image. Then the object in the image has a size in pixels, which is some percentage of the sensor size in pixels. This makes its size in mm be that percentage of the sensor size in mm. Magnification is about actual reproduction size on the sensor.
• If the total field size is the object of interest (the slide for example), then Magnification is also the size of the sensor / the real life size of total field of view.
• But Magnification is NOT otherwise the size of an object on sensor / the size of sensor (except when the object image size happens to exactly match the sensor size, example next below). Magnification is NOT about how well the object fills the frame (that frame depends on the sensor size used). The various sensor size frames simply contain the magnified object, or possibly only a cropped part of it. Sensor size is a big factor of printing enlargement, but camera lens magnification is independent of sensor size.

But speaking of copying slides and matching the sensor area, if we do know the actual sensor size in mm, then...

The magnification number will depend where your setup is between at closest focus (suggested) or at Infinity focus (because the focal length varies between those limits). Using your macro setup, photograph a horizontal millimeter ruler (at least f/16, and more is better, to have the maximum of a very small depth of field for sharpest focus at macro distances). If some dimension on your ruler fills the known sensor frame size (say it is known to be 24 mm wide), then if the full frame photo of the ruler shows ...

12 mm of ruler in sensor width is 24 mm on sensor / 12 mm real life size = 2x magnification, 2:1 reproduction.
24 mm of ruler in sensor width is 24 mm on sensor / 24 mm real life size = 1x magnification, 1:1 reproduction.
48 mm of ruler in sensor width is 24 mm on sensor / 48 mm real life size = 0.5x magnification, 1:2 reproduction.

Two sensors, 36 and 24 mm width.
Both images are 1:1 magnification on the sensors (real life size), but then the images can be shown at any viewing size, here near 3x size.

36 mm sensor width, ISO 100, f/32, 10 seconds. The sensor includes 36 mm of the cm ruler.

24 mm sensor width, ISO 100, f/32, 10 seconds. The sensor includes 24 mm of the cm ruler.

Lighting was a desk lamp, and 1:1 requires near 2 EV greater exposure, which with f/32 required 10 seconds.

Magnification: Definitions A or B

A: Mag =
Image size of object
Real object size

B: mag =
Sensor width
Width of ruler shown

Mag =
mm
mm

Magnification:

Magnification is the simple division of sizes, with two options (object size or sensor size):
1. Image size of object / Real life object size.
2. Sensor width / Width of the ruler shown.

This photo image of a cm ruler is from a macro lens set to its closest focus (which was set at 1:1). The first was used a 36 mm width full frame sensor (with distance adjusted until good focus). The viewfinder sees 36 mm on the ruler, and that computes 36/36 mm = 1x closest magnification. Or 24/24 mm is 1x too. This was 36 mm on the camera sensor, but the image shown is an enlarged picture on the current viewing screen.

To determine lens specification of closest magnification, use the closest focus and No extension tube, but use the extension tube to determine actual setup magnification. The closest magnification specification for most regular lenses will typically be limited to a value around 0.1 to 0.25x, like perhaps 0.15x (because larger requires increased focal length, which increases f/stop number, which decreases exposure. At the same aperture diameter, 1:1 reduces exposure -2 EV, 4x longer exposure.)

Regardless of whatever focal length or sensor size is used, a macro lens does 1:1 if the focus scale is set to 1:1. Focal length does determine that focused distance, and sensor size determines the outer frame size around the focused 1:1 subject size. But regardless of any focal length or any sensor size, 1:1 means that the subject image is the same size on the sensor as the real life subject size.

Extension tube magnification varies somewhat, depending on if at lens closest focus (maximum magnification) or at the Infinity setting (minimum magnification).

The viewfinder may not show exactly the full view that the photo sees. It's what the photo sees that counts.

One more time: On different cameras, 1:1 is still a constant (1:1 means the image size of an object is the same size on the sensor as the real object size), but the sensor frame size around it can be a variable field of view (depending on how much the sensor size can include). But the 1:1 size setting on the sensor is that same actual object size with any focal length (which of course may be larger than the sensor).

24 mm of ruler seen at 1:1 in a 24 mm sensor will fill the frame. But 24 mm of ruler seen at 1:1 in a 36 mm frame is again the actual mm size in the image, but 24 mm only fills 2/3 of the 36 mm sensor width.

Crop factor simply crops the field of view captured, but the sensor CANNOT change the image projected by the lens.

Reproduction Ratio: Note that 1:2 and 2:1 are very different. This ratio convention is:

Size of the image on the sensor : Size of the real life subject

1:1 lens ratio is same life size, real and image are the same size (full copy on 1x crop factor sensor).
1:1.5 lens ratio is 1/1.5 or 0.667x (2/3) magnification (full copy on 1.5x crop factor sensor).
1:1.6 lens ratio is 1/1.6 or 0.625x (5/8) magnification (full copy on 1.6x crop factor sensor).
1:2 lens ratio is an image half the size of real, 0.5 magnification (copy on 2x crop factor sensor).
2:1 lens ratio is a double size image, 2x magnification (copy on 0.5x crop factor sensor).
You can think of the : as a division: 1:2 is 1/2 magnification in the image. 2:1 is double size.

Mainstream copy:

35 mm slides will work easiest on a DSLR using a 1:1 macro lens. The 1:1 is a fixed ratio, so if at 1:1, slides smaller than the sensor create images smaller than the sensor (same size as slide). Slides larger than the sensor will have to back off some from 1:1, so to copy full size slides, a 1.5x crop DSLR sensor will use the lens near its 1:1.5 ratio setting. The macro lens is very versatile, and can be refocused to any workable ratio for larger slides at a greater distance. Many current macro lenses can do 1:1, but several older ones only do 1:2 (half life-size images). And a few regular lenses can do 1:3 (and they call it macro, and 1:3 can copy medium film size).

The 1:2 lens offers less image size and resolution than 1:1, but it may still be sufficient in some cases (with more extreme cropping). Or for 35 mm slides, a 1.5 or 1.6 crop factor will partially compensate for a 1:2 lens (with 75% or 80% image size instead of 50%. A 2x crop factor would be 100% size at 1:2.) We can't move the slide closer because the lens won't focus closer than 1:2. Or adding a regular extension tube with extension length 50% of the focal length will convert a 1:2 lens to 1:1.

Extremes:

8 mm movie film appears to be the smallest film size, 4.4x3.3 mm. A 1:1 macro lens cannot move closer to enlarge it more, because it cannot focus closer than 1:1. Small film could use normal extension tubes (between body and lens). Depending on sensor size, tubes creating around 3x to 7x (quite extreme) could be used for 8 mm film (magnification of tubes is more effective on shorter lenses). However then the resulting 20,000 to 30,000 dpi will not be very helpful, and the quality of the tiny film will likely be disappointing. The most resolution that film can supply is more like 3000 dpi, if that for the tiny film. The useful result shown may be less ratio than the maximum you might specify. A smaller sensor with larger crop factor can help reach the smallest film. The same numeric ratios give the same result sizes for macro lenses or extension tubes.

Larger sheet film or prints are much easier, and regular lenses out to 1:8 at closest focus can be computed. Specifications for interchangeable lenses normally show the Maximum Magnification at Closest Focus.

Macro Working Distance:

The camera specification for Closest Focus Distance is measured to the sensor plane, which then is only valid for that one specific closest focus distance specification. And even then, the Working Distance (subject to front of the lens) must subtract the spec for the lens length, and also subtract the mounting flange to sensor distance. Trying to compute the working distance from magnification is problematic for two reasons.
• The Thin Lens Equation is for a simple one element lens, like a simple magnifying glass. Distance is measured from the center point of that lens. But camera lenses are more complex multi-element lenses (thick lens). The angle in front of the lens is computed from one nodal point, and the equal angle behind the lens is computed from another nodal point. A couple of examples of these points is Here, see telephoto and wide angle diagrams. These points are not in the same place, and are typically somewhere inside the lens, but can be intentionally designed outside. Their precise locations are generally unknown to us. There are formulas for subject distance or focal length, but users don’t know where to measure the distances to. But using magnification is instead standard practice, and the calculation will be pretty close, and close enough.
• Internal focusing lenses don't extend the lens forward to focus closer, but they do modify the effective focal length.

Lenses vary in design affecting computation, so simple accurate measurements of actual working distance to front of lens works out to be more accurate. And here are good charts for many common macro lenses, both 1:1 and 1:2.

Numbers: Example at the calculator if copying 36 x 24 mm slide film with 1:1 lens ...

• into 6000 pixels, that is 6000/36 mm = 166.7 pixels per mm, and x25.4 is a 4233 pixels per inch scan of the film. If you can fill the pixels, it is 6000 pixels reproducing 36 mm of film, regardless of smaller sensor size (but 1:1 will not fill all the pixels if the sensor is larger than the film).
• onto a 36 mm sensor is a 1:1 copy, 100% size reproduction.
• onto a 24 mm sensor is 1:1.5 reproduction (24/36 = 0.67x reduction) onto a 1.5x cropped sensor, requiring 1.5x copy distance. That current reproduction on the sensor is 6000/24mm = 250 pixels per mm on the sensor, but which requires 1.5x greater enlargement to subsequent viewing size. Printed 24 inches (600 mm) is a 600/24 = 25x enlargement of sensor (16.7x of film) which will be 6000/600 mm = 10 pixels per mm or 250 pixels per inch on paper. Possible because the scan created 6000 pixels from 36 mm of film (4233 pixels per inch of film).

If copying film size equal or larger than your sensor size, then you will be able to fill your frame with a 1:1 lens, at least with one dimension of it (both depends on aspect ratio of film matching your sensor). This calculated output image size assumes you will "fill the frame" with one dimension of the slide image. Not fully filling the frame width would be less dpi. Overfill (causing cropping) would be greater dpi. Dpi shown is "scan resolution" ("pixels per inch" of film, just like a scanner), and it also shows "pixels per mm" of film.

If copying film smaller than your sensor, then with a 1:1 lens, your largest copy will be 1:1, and that resulting image will be smaller than your frame (so subsequent cropping will be necessary). This "fill the frame" magnification is not possible for the tiniest film (since most macro lenses only go to 1:1). Filling the frame with film smaller than the sensor (small film or large sensor) requires exceeding what 1:1 magnification can do. Then (if crop factor is entered here) these small sizes instead are computed using a 1:1 lens at 1:1 (frame is not filled). This computation of copying smaller film does need an accurate crop factor (see determining crop factor). Otherwise, without crop factor, filling the specified frame is all that it can assume, but which is not likely possible for 1:1 and smaller film.

There is Magnification and there is Reproduction Ratio (like 1:1). Magnification is (size of image : real life object size), and Reproduction Ratio is the reciprocal (Magnification 0.5x is Reproduction Ratio 1:2). Camera images are typically a size reduction, normally significantly smaller than 1:1 (like 1:100 or 1:1000). We may take a picture of something large on a few mm of sensor, which maybe is a reduced reproduction of 1:100, which is a magnification of 0.01x. But a magnification of greater than 1 is larger on the sensor than in real life. Which might be accomplished by adding extension tubes, but normally a macro lens does not focus larger than 1:1.

When we used film, we could hold the processed film in our hand, and see that image for a clear understanding about it's size. We can't see the actual sensor image in a digital camera, but it's exactly the same size concept, size at the sensor, created by the lens. The reproduction ratio 1:1 means the external field of view (in millimeters) is exactly equal to the sensor size.

A macro lens at 1:1 means that the subject image is full real life-size on the sensor. A full-frame camera copying a 35 mm slide would need a 1:1 macro lens, to make a full size copy of the slide. At 1:1, a 36x24 mm slide size exactly matches a full frame 36x24 mm sensor size.

An APS or DX size DSLR has a smaller sensor (smaller than the 35 mm slide), so cannot use as much as 1:1 (for this slide copy). The 1:1 lens magnification is the SAME subject size on any sensor (it's a lens property, NOT a sensor property), but the cropped sensor does seriously crop the full frame view of it. The 35 mm slide is larger than the cropped sensor size. A 1.5 crop sensor does need 1:1.5 reproduction (for a 35 mm slide), so the slide is held a little farther in front of the lens (to be seen smaller). Then at 1:1.5, a 36x24mm slide size matches a 24x16 mm sensor size.

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