 Bob Cammarata |
Macro-Math Question? Having dabbled in macro photography for quite some time, I'm familiar with how magnification ratios are determined when my lenses are focused at infinity and extended with extension tubes or a bellows assembly. But I'm not sure how to accurately calculate life-size ratios when I use a reversed 55 mm on a fully extended bellows (190 mm) with the lens also fully extended to its closest focusing distance. ...Then, there's the 1.6 "crop factor", which comes into play when I use my digital camera. That's usually when my brain starts to hurt and I just take an educated guess.
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Samuel Smith |
boy,short of a brain implosion,i just want to tag along,sam
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Alan N. Marcus |
Hi Bob, I too get headaches making optical calculations. You should know I recognize your pain. For the edification of those who don’t have a clue about what you are asking: Since the typical camera lens is designed to image from a 3 dimensional world and project onto a flat field, it is challenged when asked to image at extreme close-up distances. One countermeasure is to use a reversing ring and mount the camera lens backwards. Advantages: 1. Spaces the lens even further forward. 2. Improves performance as depth-of-field is nearly nonexistent, imaging is improved as the rear element is designed to operate on a flat screen film/chip. 3. The effective focal length of a reversed lens is shorter thus magnification at any given extension is higher. There are many ways (formula) to calculate magnification. M = image height divided by subject height. M = Lens to focal plane distance divided by lens to subject distance. M = lens to focal plane divided by focal length, minus 1. Lens to focal plane distance = magnification +1, multiplied by focal length. All measurements involving the lens position are taken from the rear nodal. Unlikely this spot will be marked on the lens barrel. Unlikely it will be in the middle i.e. halfway between front and rear element. To do serious math you need to find this point. Place the dismounted lens on your desk; I place it on a book. Place an illuminated mm ruler ahead of the lens. Best use a spot to illuminate the ruler. A bright flashlight works. Place a white paper screen behind the lens. With luck you can adjust the mm ruler distance to lens and target screen to lens distance to achieve a projected image on the screen that is life size i.e. unity or 1:1. When you achieve magnification 1, check using a duplicate ruler and measure the size of the projected image. When M 1 is achieved, measure distance, screen to subject. This distance will be 4x the actual focal length. The rear nodal will be in the center of this setup i.e. half way between ruler and screen. The method also defines for you the lens position to achieve 1:1. I often resort to a simpler method. Using the camera with lens mounted I set-up a mm ruler as the subject. As you focus and adjust camera to subject distance you can see and maybe measure the image on the viewing screen. On a full frame you achieve 1:1 when you can count 36 mm rulings as seen in the viewfinder. Keep in mind the digital might have a viewfinder magnification factor. Say it’s 95%, you will see only 34 markings. On a digital with a 1.6 crop factor, this translates to rectangle that is 1/1.6=0.63 or 63% of a full frame. Thus the chip is 24 x .63 = 15mm by 22.7mm. Now you known the chip is about 22.7mm long. If you achieve 1:1 you will see 22 or 23 markings. Keep in mind that your viewfinder might not give a 100% view, most are 95% thus you count 21 ½ mm markings for life size i.e. 1:1. Think this method will suffice as you likely don’t need to be all that precise. One more thought: A macro lens is corrected for unity and designed to image flat to flat. Alan Marcus (marginal technical gobbledygook)
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Bob Cammarata |
The way I understand it, bellows lifesize magnification ratios are computed by dividing the distance-to-subject (amount of extension in mm) by the lens focal length when focused at infinity. In other words, with a 55 mm lens mounted normally onto a bellows at 190mm of extension...190/55=3.45 (or approx 3 1/2X-lifesize is achieved in 35 mm format). How does reversing this lens affect the magnification ratio?
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Alan N. Marcus |
Stated differently: The focal length engraved on the lens barrel describes the distance from the rear nodal of the lens to focal plane when imagining a subject at infinity. For subject distances closer than infinity the working focal length is elongated. Thus the necessity to rack the lens forward to achieve close focus. Life size – magnification unity or magnification 1 or 1:1 is achieved when the rear nodal-to-focal plane distance is 4 times the focal length engraved on the lens barrel. Thus for a 55mm lens, when focused at infinity, the lens’s rear nodal will be 55mm from the film/chip (focal plane). At magnification 1 i.e. unity (1:1), the subject-to-focal plane distance will be 4 x 55 = 220mm. The rear nodal will be 110mm from the focal plane and 110mm from the subject. For unity (life-size) this 4x relationship subject distance to focal plane distance is absolute and independent of format size. As an example, for the 4x5 inch view camera fitted with a “normal” focal length 6 ½ inches (165mm). To achieve unity the subject to focal plane distance is placed at 660mm. For miniature cameras and especially SLR’s, the rear nodal is likely shifted rearward of center as referenced by the lens barrel. This is true because the optician is faced with the problem of providing clearance for the mirror travel. A rearward nodal shifts the lens and barrel forward away from the mirror. For the telephoto, a shorter barrel sells better. Everyone wants a more compact telephoto. Thus in a true telephoto design, the rear nodal is shifter far forward, often it falls outside the lens. This design shortens to overall length of the barrel. How shifted: If a miniature camera lens is not likely to have a rear nodal that is symmetrical with the lens barrel. Repositioned backwards, its working focal length will usually be shortened. A shorter lens gives more magnification at a given extension. Because every lens design is different I don’t think a specific multiplying factor can be utilized. Alan Marcus (more marginal technical gobbledygook)
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Alan N. Marcus |
I made an error: Life size – magnification unity or magnification 1 or 1:1 is achieved when the rear nodal-to-focal plane distance is 4 times the focal length engraved on the lens barrel. Life size – magnification unity or magnification 1 or 1:1 is achieved when the subject-to-focal plane distance is 4 times the focal length engraved on the lens barrel. I will stand in the corner for 1 hour with dunce cap on. Alan Marcus
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Bob Cammarata |
Thanks Alan for your detailed response. You've given me much to absorbe. (...now, if I could only remember where I left that bottle of Tylenol... :(
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