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Magnification Ratios

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Close-up/Macro photography

 


 

Magnification Ratios

 


 

 

Photography is a discipline that encompasses many different aspects. One that many encounter whatever kind of images they take, is that where closer focusing and higher than normal image magnification is involved. This might be to capture a small portion of a relatively large subject to reveal some aspect of the details, or to fill the image frame with as large a view as possible of an object that is quite small in real life for the same purpose.

 

Although the general principles surrounding this kind of photography hasn't changed with the advent of digital cameras, the approach to it needs to in some respects. This is because the magnification that is involved is not usually defined in measurement terms, but in ratio. The reproduction ratio being that between the size of the subject in real life, and the size of it on the film/sensor, so the ratio indicates what size the subject image will be on the film/sensor used by the camera, in relation to the subjects real life dimensions.

 

Whilst this continues to be the classification used for the magnification ratios that DSLR lenses can achieve it isn't for digicams, where as a general rule the minimum distance to which focusing is possible is used instead. Neither method is really satisfactory as a means of indicating what can be achieved with a particular digital camera because of the wide range of different sensor sizes now in general use, and the impact that this has on the final result, for it's not the magnification ratio of an image or how close to a subject you can get that really matters, important though they are in some respects, but the actual area that is covered. This is especially so when attempting to make evaluation comparisons between different cameras, and the methods of how it can be undertaken.

 

We will try and cover all the general aspects of taking magnified images with digicams and DSLR's, and the different ways it can be approached depending on the type of digital camera used, to produce comparable images. We'll begin with the terms used to describe the various levels of magnification, the calculations used to determine magnification reproduction ratio and area coverage, and what they mean in relation to taking shots with various digital cameras. Then look at the equipment that can be used depending on the camera involved.

 

There is however one aspect that stands out, one clear advantage the use of any digital camera has, the almost instant ability to review images taken and make any necessary adjustments needed if the result doesn't match up to need or expectation. This is of particular importance when confronting situations where high and very high magnification is involved and problems are encountered with obtaining acceptable image quality.

 

 


 

 

Magnification terms & ratios

 

 

Today and for some years past the term 'macro' has generally been used as an all-encompassing description when referring to higher magnification photography. Any camera or lens that can focus closer than that normally expected tends to carry the label 'macro' somewhere. Digicams often have a 'macro' mode. But it is really the incorrect use of a term meant to refer to a specific magnification ratio range, so we'll start by looking at the particular terms and how the current situation has arisen.

 

There are three main terms that should be used to describe the general magnification ratio's used in photography and these are; Close-up; Macro; Photomacrography. Close-up photography is concerned with magnifications between the reproduction ratio 1:20 (or 0.05x), and what is called 'life-size', 1:1 ratio (or 1x). Macro photography covers the ratio's from 1:1 to 25:1 (25x). Photomacrography covers those from 25:1 onwards to 100:1 (25x to 100x), those beyond these being the exclusive province of the microscope. Most camera users rarely if ever stray beyond the bounds of close-up photography, and of those that do, fewer still use ratio's much beyond 5:1 (5x). As a general rule those beyond 1:1 are usually most often undertaken for Natural Science subjects, and beyond 5:1 in particular, for specific scientific purposes such as forensics and medicine.

 

It's perhaps helpful to understand at this stage that this type of photography has for a considerable number of years been almost exclusively concerned with the use of the 35mm full frame film format, and specifically with 35mm SLR's. It has been undertaken with the larger 120 film format and medium format cameras, but not to quite the same extent, and not with quite the range of specialized equipment that has been produced for 35mm use. For this reason most of the calculations that have been used, and the results obtained, have assumed it's use. It has, as far as we are aware, never been generally undertaken with the smaller film formats. As a result it has long been accepted that the use of 35mm produces the best results in terms of the scale of magnification possible. With the arrival of digital cameras with much smaller sensors this is now no longer the case.

 


 

A knowledge of magnification ratio's helps in the basic understanding of close-up and macro photography, and how the relationship between using digital cameras with different sensor sizes affects what eventually results when either the same or different ratio's are used.

 

The definition of the magnification or reproduction ratio, R is the size of a subject on the film/sensor against the size the subject is in real life: 

R =

size on film/sensor

actual subject size

 

So when a subject is represented on film or sensor at the same size as it is in real life, millimetre for millimetre, then it is at a ratio of 1:1, commonly called life-size. We'll try and illustrate this as simply as possible by using our standard lens test chart, which is marked with a few sensor sizes on it, and some shots of a steel ruler.

 

Firstly here is a view of the whole test chart. It's nothing special, just a basic graph of solid lines at 25mm intervals, with dotted lines every 5mm, ink-jet printed onto A4 sized heavy-weight matt photo paper. The chart is not used to test lens resolution as such, (although it's a useful indication), but things such as lens image quality in respect of distortion, corner shading etc, as well as minimum focus distance (MFD) from the subject to the focal plane, minimum working distance (MWD) from the subject to the end of the lens, and the actual image magnifications that result in terms of actual area coverage.

 

 

                       full chart                 

 

As well as including our website page header, there are also outlines representing the actual size of a 35mm film frame/full frame sensor (red), the common Pentax/Nikon/Sony 1.5x APS-C sensor size (black), and the 1.1/8" digicam sensor size (green). It is the area inside the outlines that is the actual sensor size, and is a interesting and stark illustration of the difference in size that exists between the basic sensor sizes.

 

 close crop of sensor size outlines

 

Okay, now if it were possible to take images with all the cameras with these sizes of sensors with lenses that allowed a 1:1 magnification ratio to be used, a full frame DSLR, a APS-C sensor DSLR, and a 1.1/8"sensor digicam, these are the images that would result. Linear dimensions and area coverage that match those of the respective sensors in each camera.

 

                      full frame/35mm                           APS-C/1.5x                                1.1/8" digicam

 

As you can see the full frame camera image thus covers an area of 36x24mm, because that's the size of the sensor. Likewise the APS-C covers 24x16mm because again that's the sensor size. And the digicam image covers just 7.18x 5.32mm, because, once more, that's the size of the sensor.

 

Here is the same magnification, this time using a steel ruler as the sample image. This makes an even starker and perhaps clearer comparison. 

 

                    full frame/35mm 1:1                        APS-C/1.5x  1:1                       1.1/8" digicam 1:1

 

Now whilst it is perfectly possible to obtain 1:1 ratio images with most DSLR's of whatever sensor size, from 4/3rds up to 35mm full frame, there is no digicam that we know of that can produce an image magnification of the 1:1 ratio that has been shown, (not even in the 'super macro' modes some are credited with). These images have been produced purely to show the relationship between image sizes from different sensor sizes depending on the magnification ratio used.

 

For further comparison here are three images with the same area coverage on each sensor. That covered by a 35mm full frame sensor at 1:1 ratio. However, the reproduction ratio's needed to achieve them vary widely between the different camera sensor size types as you can see, and this is where a lot of the advantages/disadvantages and the subsequent confusion surrounding magnification ratios arise.

 

         full frame/35mm - ratio 1:1 (1x)   APS-C/1.5x - ratio 1:0.66 (0.66x)  1.1/8" digicam - ratio 1:0.20 (0.2x)

 


 

 

Magnification ratio's in area measurement terms

 

Now that the relationship between different sensor sizes is a little bit more understandable lets turn our attention to what magnification ratio's means in practical measurement terms. Because it's what happens in actual practice and general day to day use with digital cameras that we are really interested in.

 

At a ratio of 1:1, and taking the steel ruler above as an illustration, each millimetre of the ruler will be reproduced at the same size on the sensor, at 1mm, actual size. This is why the term 'life-size' is used, because the reproduction is actual size on the sensor, the size it is in real life. A ratio of 1:2 is 'half life-size', and in this case each millimetre of the ruler will be reproduced on the sensor at 0.5mm. A ratio of 1:4 is a 'quarter life-size', and here 0.25mm will represent each millimetre of the ruler on the sensor. Thus if the reproduction is 1:2 ratio, half life-size, then on a 35mm full frame sensor 36x24mm, 72mm of the ruler will be captured. More of the ruler, a smaller magnification. At a quarter life-size, 144mm will be captured.

 

Another way of writing these ratio's as fractions is 1x for 1:1, 0.5x for 1:2, 0.25x for 1:4, and so on. You will see that these figures represent the measurement size that results from the magnification used. Camera and lens makes often use these figures when referring to maximum reproduction ratio's for DSLR lenses. A lens may be classed as having a maximum ratio of 0.34x for example, which usually means absolutely nothing to the average camera user. But we now know that this means that at the lenses maximum magnification 0.34mm will represent on the sensor every 1mm of an object in real life.

 

However, it's important to understand that these magnification ratio figures refer to linear measurement, and not area coverage. If we again take the size of the 35mm film frame - 36x24mm - as the example, at the 1:1 ratio it will fill the image frame of a full frame sensor. But at 1:2 ratio, half life-size, it will cover just a 1/4 of the frame area, and at 1:4 ratio, a quarter life-size, it will cover just 1/16th of the image frame area. So in real practical visual terms there is a large difference in subject size reproduction for different magnification ratios.

 

 

                Life-size - 1:1 or 1x                   Half life-size - 1:2 or 0.5x          Quarter life-size - 1:4 or 0.25x

 

 

This factor assumes even greater importance when considering and comparing the actual area coverage rather than the magnification performance of one camera type and sensor size against another as we have shown earlier.

 

 


 

 

Calculating area coverage

 

We have stated that using magnification ratio's to indicate close-up/macro capability isn't really totally satisfactory in these days of wide differences in sensor sizes because of the variations in results that occur, and that area coverage should be the yardstick. In the current absence of such information from camera and lens makers the only recourse is to calculate it yourself.

 

You can make quick and easy mental comparisons between DSLR's in the sense that we know that smaller sensors can produce larger magnification that bigger ones, so can use lower ratios to obtain the same result, whilst bigger ones need to use higher ones. As a rough ready-reckoner 35mm full frame format DSLR's need 50% higher magnification than APS-C sensor DSLR's for comparable coverage, so 1.5x to equal 1x, and 100% higher to match 4/3rds DSLR's, 2x to equal 1x. Or to put it the other way around, 4/3rds DSLR's only need 0.5x to match 1x from a 35mm FF DSLR whilst APS-C needs 0.66x. You need the lens magnification ratio and exact sensor size for any other comparison, but at least this can be undertaken and the result calculated.

 

This is rather better than the situation that exists with most digicams, where only focus distance is generally given, for there is no way to determine magnification ratio or area coverage from this alone. In fact the only way this information can be obtained if the camera maker doesn't provide it, is by practical testing of the relevant digicam.

 


 

We have seen that the effect of a magnification ratio in linear measurement terms is described in whole or partial fractions of a millimetre, 0.25x, 0.5x, 1x etc. To calculate the area coverage that results you therefore need to divide the sensor size measurements, length & breadth, by the magnification the lens used provides and multiply the results. To do this you then obviously need to know not only the MR ratio of the lens, but the sensor size.

 

Here is a table listing the main current DSLR nominal sensor sizes, which sometimes vary slightly between individual cameras.

 

 

Type Size Area in mm's
35mm full frame  - Canon/Nikon/Sony 36mm x 24mm 864 sq mm

APS-C - Pentax/Nikon/Fuji/Konica-Minolta/Sony

24mm x 16mm 384 sq mm
Canon EF-S 22.5mm x 15mm 338 sq mm
Sigma 20.7mm x 13.8mm 286 sq mm
4/3rds 18mm x 13.5mm 243 sq mm

 

 

And here is another listing those sensor sizes and the area coverage at a number of commonly found MR ratios many DSLR lenses have. Under the sensor size type listing in brackets is the lens multiplication factor - LMF - relating to the sensor size and used to calculate the 35mm equivalents in lens focal lengths. We've included this as another comparison indicator because as this relates to area sensor size, when you look at what each respective DSLR sensor size achieves, this is the magnification ratio the 35mm full frame format has to produce to equal it. So for example when a 4/3rds DSLR uses 0.25x a FF DSLR needs to achieve 0.5x, (0.25x times 2x) to match the performance.

 

 

Type Magnification  Coverage Area in mm's
35mm full frame 0.25x 144mm x 96mm 13824mm
0.34x 106mm x 71mm 7526mm
0.5x 72mm x 48mm 3456mm
0.75x 48mm x 32mm 1536mm
1x 36mm x 24mm 864mm
       
APS-C

(1.5x)

0.25x 96mm x 64mm 6144mm
0.34x 71mm x 47mm 3337mm
0.5x 48mm x 32mm 1536mm
0.75x 32mm x 21.5mm 688mm
1x 24mm x 16mm 384mm
       
Canon EF-S

(1.6x)

0.25x 90mm x 60mm 5400mm
0.34x 66mm x 44mm 2904mm
0.5x 45mm x 30mm 1350mm
0.75x 30mm x 20mm 600mm
1x 22.5mm x 15mm 338mm
       
Sigma

(1.7x)

0.25x 83mm x 55mm 4565mm
0.34x 61mm x 40.5mm 2470mm
0.5x 41.5mm x 28mm 1162mm
0.75x 28mm x 18.5mm 518mm
1x 20.7mm x 13.8mm 286mm
       
4/3rds

(2x)

0.25x 72mm x 54mm 3888mm
0.34x 53mm x 40mm 2120mm
0.5x 36mm x 27mm 972mm
0.75x 24mm x 18mm 432mm
1x 18mm x 13.5mm 243mm

 

 


 

 

It's a rather unfortunate but inescapable fact that there is no easy way to determine digicam close-up/macro image performance or to compile comparison tables as those above. Only by practical testing is it possible to discover individual digicam macro performance as we have already indicated. This is due simply to the basic design principles of digicams with their integrated all-in-one lenses made in many cases to cover as wide a usage range as possible, from wide angle to telephoto. Whilst there are many commonalities between the various cameras as far as general design and overall performance goes, there can also be wide differences in what any particular lens they have has been equipped to produce. Apart from the restraints imposed by basic lens optical design principles there is no common standard that has to be observed or adhered to, it's entirely up to the camera maker as to what range and level of image performance any one digicam lens may deliver. 

 

Thankfully some camera review websites sometimes include macro image performance in their reviews of digicams, including focus distance, area coverage, and image distortion levels, and these can be used to get a good idea of what any particular digicam is capable of in respect of close-up/macro images. We've compiled a small table as an example of what a few can achieve with the scant information we have been able to gather, but it gives an idea of the range and scope, which does, as you can see, vary enormously. 

 

 

Digicam

 coverage wide angle

wide 

(super macro)

 coverage

telephoto

focus distance
Canon  A95 56 x 42mm

-

87 x 65mm 5cm - ?cm (w-t)
Epson 3000z 80 x 60mm - 80 x 60mm 6cm - 20cm (w-t)
Canon G7 24 x 18mm - 102 x 76mm 1cm - 50cm (w-t)
Fuji S9500 91 x 68mm 38 x 28mm 79 x 59mm 10cm - 90cm (w-t)  
Fuji S100fs 79 x 59mm 38 x 28mm ? 10cm - 90cm (w-t)  

 

Camera lenses usually give their maximum magnification at their minimum focus distance, which in the case of most zoom lenses is at their longest focal length. But you can see here that this does not hold true for digicams, where not only can the reverse often occur, with the shortest focal length giving the largest magnification, but the the focus distance alters markedly too, there not being a constant minimum focus distance as with most DSLR lenses, but ones that vary depending on the focal length.

 

We'll deal with the consequences that arise from this, for severe problems can often exist as a result, when we look at actually taking close-up/macro shots.

 

 


 

 

Calculating magnification ratios

 

 

If you find yourself in the situation where you have a subject whose size is known, and you want to discover the magnification ratio that is needed to capture it to fit the image frame as fully as possible, this can be calculated. We'll use some different sized items to illustrate the calculations used, and the different magnifications needed depending on the particular digital camera type and sensor size involved. For when you get down to small objects and high magnification ratio's, a small difference in subject size can make a substantial difference to the ratio needed.

 

For our subjects we will use postage stamps. These are an everyday item that also gives rise to a hobby for many, stamp collecting. Many stamp collectors like to make records of their stamp collections by photographing the individual stamps they have, either for their own pleasure, or to share the images with other collectors for various purposes. 

 

Although they vary in size, as a rule postage stamps aren't very big in the general scheme of things, and those with lower values or meant for the smallest letter sizes tend to be smaller than most. So the first example is a British Post Office/Royal Mail stamp of 10p value. It measures approx 25x21mm over the perforations. 

 

 

To calculate the magnification needed to fill an image frame with the subject at the best possible fit, allowing for different format ratio's, it is necessary to divide either the width or height of the sensor used in the camera by the width or height of the subject. As this stamp has a ratio of 6x5, and camera sensors are either 3x2 (most DSLR's), or 4x3 (most digicams), in this case it's the width dimensions that are used.

 

For a full frame sensor DSLR of 36x24mm this means dividing 24 by 21, which gives a ratio of 1:1.143 or 1.143x, so more than the 1:1 ratio is needed to completely fill the frame to the maximum since the stamp is smaller than the size of the sensor. Using a APS-C sensor DSLR with a 24x16mm sensor, dividing 16/21 gives a magnification ratio requirement of 0.76x, whilst a 1.1/8" digicam sensor camera at 7.18x5.32mm only needs a magnification of just over a quarter life-size at 0.253x. 

 

 

Now lets move on to a slightly larger subject and see what difference emerges. This British Post Office/Royal Mail 16p stamp was issued to commemorate the centenary of the Greenwich Meridian in 1984. It measures 41.5x30.5mm over perforations and is approximately 7x5 ratio.

 

 

As it is larger, lower magnifications are needed. The calculations for 3x2 ratio format sensors are the same as the other stamp, width ways. For full frame DSLR capture, a ratio of 0.79x results, and for APS-C DSLR's, 0.52x, just slightly over half life-size. The ratio for the 1.1/8" digicam needs to be calculated using the length rather than the width as this reaches maximum size first on a 4x3 ratio sensor. Here a 0.17x ratio results.

 

Similar calculations are used if you just want to know the magnification ratio that was used to achieve a particular image size. Say for example you end up with an image that covered an area of 84x63mm using a 1.1/8" sensor digicam. Then simply divide the sensor width, 7.18mm by the width of the image coverage, 84mm. This results in an reproduction ratio of just 0.085x. 

 


 

We hope that perhaps the relationship between magnification ratio and sensor size is now slightly clearer. That as the sensor size gets smaller, a lower magnification ratio is needed for identical size image reproduction, or the larger the sensor, the higher the magnification needed. To put it another way, the smaller the sensor, the larger the reproduction can be for the same magnification. 

 


 

Now we'll move on to more practical matters - the actual taking of images and the equipment that can be used

 


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