My Search for an Inexpensive Macro Test Target

Introduction
Two previous articles have examined the calculation of resolution (approx. 9% MTF) for the Canon SX30 35x 14 MP camera, considering the combination of lens and sensor resolution.  The result are similar for the Canon SX40, which has the same lens but only 12 MP in the sensor, resulting in a slight decrease of resolution.  Correction October 18/12:  Sensor width was changed from 6.17 mm to 6.01 mm (see Reference 6).
This made minor corrections to the Magnifications, Sensor Resolutions, Total Resolutions and Object Resolutions in Table 1 of the Appendix.  Correction November 30:  Sensor width was changed from 6.01 mm to 6.20 mm (see Reference 6).  This made minor corrections to the Magnifications, Sensor Resolutions, Total Resolutions and Object Resolutions in Table 1 of the Appendix.

  • The first article [1] examined the resolution of the SX30 and SX40 at full optical zoom (840 mm equivalent) compared with that of Compact SLRs.  The article concluded that a Compact SLR would require at least a 400 mm focal-length lens to surpass the resolution of the SX30 and SX40.
  • The second article [2] revised the resolution formulas so that they could be used for close-up objects.  The resolution of Macro at a distance of 1 cm was then compared with with that of TeleMacro at 1 ft and at 50 inches.
  • The present study uses the same resolution formulas as [2], which examined Macro at 1 cm from the lens barrel.   The present study examines how the resolution varies for objects at -4 mm, 0 mm, 5 mm and 10 mm from the front of the lens barrel.  (-4 mm is touching the lens.)


Calculation of Macro Resolution
The following steps were taken to calculate Macro resolution vs distance:

  • Camera Settings: The SX30 was set to L format (4320 x 3240 pixels) for maximum resolution.  Aperture-Priority mode was selected in order to select the aperture for each resolution measurement.
  • Calibration (Appendix ): A millimetre scale at carefully measured distances from the lens barrel was photographed in order to calibrate the magnification for each distance.
  • Calculation of  Resolution: The magnification was then used to calculate the object resolution.  This calibration procedure  are described in the Appendix and the results are given there in Table 1.  The resolution for each distance is calculated from Equations 1-5 of [2] , based on the aperture and magnification.  The results of the resolution calculations are also given in Table 1.  The line-pair per mm resolutions are given for the lens, sensor and the total.  The resolution on the target is provided in millimetres.  (Multiply by 1,000 to get microns.)  From the table, it can be seen that the calculated resolutions range from 14 microns when the object is touching the lens to 27 microns when the object is 10 mm from the front of the lens barrel.  Ideally, it would be good to measure the resolution for each case, using a  commercial Macro test target.  The following paragraphs describe my search for a less expensive test target.


Search for an Inexpensive Macro Test Target
My first stop was the Internet, to look for a  test target that is specifically designed for Macro testing.   Unfortunately, such targets cost at least $200 once taxes, duties and shipping are included [3,4].  Discussions on forums turned up other people looking for something less expensive.  Some suggestions for targets included blowflies and EPROM chips with the window removed.  I decided to try to make a small version of the USAF test target.  For telephoto testing, I already had a pdf file of the USAF 1951 test chart obtained free from Takinami [5].  Using my printer, this pdf file produced a  full-page target with sharp edges, which was perfect for telephoto purposes (unlike jpeg files that I had tried, which produced messy edges).  The pdf file also looked promising because it could be expanded many times on the computer screen with the smallest elements remaining sharp.

Printing pdf file on my own printer:  The printer specs claimed "up to 1,200 dpi effective output" which translates to 600 line-pairs per inch (line-pair spacing of  0.042 mm).  Looking at Table 1, that would be good enough to test Macro at a distance of 100 mm.  Unfortunately my actual printer output was only about 125 line-pairs per inch, which was useless for Macro testing.

Printing pdf file at local drugstore and at a printers:  My next attempt at producing a Macro test target was to take the pdf file to my local drugstore to get a 4"x6" print.  Unfortunately the drugstore could not process pdf files.  Next, I took the pdf file to a professional printer who ran off a 4"x6" print.  The 3-bar pattern could be seen down to 250 line-pairs per inch, which is still not good enough for Macro testing.  I was beginning to understand why companies are able to charge so much for a Macro test target.

Making a jpg test target for printing at the drug-store: My next attempt was to make a test chart using PhotoShop by painting the bar patterns a pixel at a time, with the bars of the smallest test pattern only 1 pixel wide.  I set the jpg compression to 12 for the highest quality and took the file to the drugstore for a 4" by 6" print.  The 3-bar pattern of 150 line-pairs per inch (line-pair spacing of 0.169 mm) was visible, but not clean enough for use as a test target.  I don't know what print quality is available from other photo processors, but this quality seems rather poor to me.  Looking at Table 1, the resolution of Macro can be 0.014 microns on the object.   To see this detail in a photograph printed at my drugstore, I would have to ensure that the printed image was more than 10 times larger than the actual size of the object, or probably even larger considering that the 150 lp/inch output was much poorer than 50% MTF.

Macro Resolution Test Results
I finally discovered that light-bulb filaments might make a somewhat suitable Macro test target.  Figure 1 shows the helical filaments from an automobile headlamp.  The filaments are wound helically like a coil spring.  The top filament has approximately 12 coils or cycles per millimetre and the bottom filament has approximately 5.  Notice, in the lower filament, how the parallax between the front and back of the helix periodically blocks the light reflected from the graph paper and partially obliterates the contrast in these regions.

 Figure 1: Automobile Headlamp Filaments 12 and 5 cycles per mm

 
The finest filament that I have found to date is from a Noma 4-Watt night-light.  I put the night-light into a canvas bag and broke it in a vise.  Then I took a portion of the filament about 1 cm long and taped its two ends to a piece of graph paper with 1-mm divisions.  The number of coils or cycles per millimetre can vary, especially if portions of the filament get stretched but, after mounting my sample and photographing it, I determined that it had 41 +/- 1 c/mm (cycles per mm, which is the same as line-pairs per mm) or a line-pair separation of 0.024 mm.  Looking at Table 1, this is close to the calculated Macro resolution for an object 5 mm from the front of the lens barrel.

Using my 41 c/mm filament test-target: The target is not ideal for a number of reasons: Firstly, the wire thickness is larger than the space between the coils, which will tend to worsen the measured resolution (as compared with a commercial test target).  Also, the contrast is not black and white, which will also tend to worsen the measured resolution.  I tried various types of lighting:  Front lighting tended to make the wire look silvery with dark gaps between the coils, while sunlight, transmitted through the graph-paper backing, made the wire look close to black and the gaps close to white.  This back-lit option seemed to give the best contrast.  The following 4 photographs are 100% crops showing the filament and two of the 1-millimetre squares behind it.  The Object-to barrel distances are: -4 mm (touching the lens), 0 mm, 5 mm and 10 mm:

 Figure 2: -4 mm (41 c/mm filament touching the lens)

 Figure 3: 0 mm (41 c/mm filament at end of lens barrell

 Figure 4: 5 mm (41 c/mm filament 5 mm

                from lens barrel)

Figure 5: 10 mm (41 c/mm filament 10 mm

              from lens barrel)



Conclusions
These photographs demonstrate results that are in approximate agreement with the resolution measurements of Table 1 of the Appendix.  The resolution for the target touching the lens is slightly better than for the target at the end of the lens barrel.  For a target distance of 5 mm from the lens barrel, the filament coils are just resolved (approx. 9% MTF) over parts of the filament length.   Parts of the filament  are not resolved, likely a result of parallax, reducing the contrast in some areas.  For a target distance of 10 mm from the lens barrel, the filament coils are not resolved anywhere.

At maximum optical zoom, I reported a calculated resolution of 30.7 microradians compared with a measured value of 30 [1].  At this zoom, the resolution is limited mainly by lens diffraction, and calculated resolution matches the measured value fairly well.

In this study, both the calculated and measured Macro resolution at a target distance of 5 mm are approximately 41 c/mm (24 microns, 1050 c/inch).  For Macro, the resolution is limited mainly by the sensor.  For an ideal target, the measured value might be expected to be a little better than calculated.

The resolution equations that were used for Macro here can also be used for telephoto.  Indeed, for large object distances, the  equations reduce to the same equations as those used for telephoto in [1].  It is encouraging that the same equations produce a good match to test results for the SX30, both for Macro, where the sensor limits the resolution, and for full telephoto, where lens diffraction limits the resolution.

What can be said with some certainty about the resolution of the SX30 is that, for full optical zoom some 30-microradian detail is visible [1] and that, for Macro at 5 mm from the lens barrel, some 24-micron detail is visible.   Assuming that the equations have at least the ability to extrapolate from a distance of 5 mm to a distance of -4 mm,  some 14-micron Macro detail should be visible when the object is touching the lens.  I would expect that, with an ideal target, the actual resolution might even be a little better than calculated.  To prove it, I need to find a new test-target.


References
[1] Detail of SX30/40 vs Compact SLR by Stephen Barrett, June 17, 2012:  http://www.dpreview.com/articles/4110039430/detail-of-sx3040-vs-compact-slr


[2] Macro vs TeleMacro with SX30/40  by Stephen Barrett, August 27,2012: http://www.dpreview.com/articles/8819494033/macro-vs-telemacro-with-sx3040

[3] Danes Picta Universal Test Target FSR2R with ISO2 pattern (12.5 to 250 cycles/mm) and USAF pattern (4 to 228 cycles per mm); Price: E150 (150 Euros)    http://www.danes-picta.com/


[4] Thorlabs 1951 USAF Square Resolution Test Target R3L3S1P    3"x3"   max resolution  228 line-pairs/mm  (4 microns); $160      http://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=4338


[5]   USAF 1951 Test Target from Takinami:   http://www.takinami.com/yoshihiko/ph..._test/USAF.pdf

[6]  Canon Specifications for SX30 IS: http://www.canon.ca/inetCA/arcproducts?m=gp&pid=4812#_030 October 16, 2012 Correction: The specifications say there are approximately 14.5 total Megapixels on the 6.17 mm x 4.55 mm sensor.  The pixels in a photo are 4320 x 3240 pixels = 14.0 Megapixels. in the ratio 4:3.  The frame size used on the sensor is then 6.01 mm x 4.51 mm. 
November 30, 2012 Correction: The sensor dimensions were calculated according to the following method provided by Steen Bay: http://forums.dpreview.com/forums/thread/3342545#forum-post-50361878  ?If we compare the actual FL and the equivalent FL (4.3-150.5 mm vs. 24-840 mm) we'll get a 5.58 crop factor, and if we divide the diagonal of a 24 x 36 mm sensor (43.27 mm) by 5.58 we'll get 7.754 mm, meaning that the SX30 sensor should be app. 6.20 x 4.65mm.


Appendix: Macro Calibration of Magnification and Resolution

The magnification M is the ratio of the image size on the sensor to the object size.  The magnifications and locations of principal points were determined by photographing a mm-scale ruler at carefully measured distances.  The magnifications were calculated by making measurements of the image size on the computer screen corresponding to a given number of millimetres on the object scale.  The corresponding actual image size on the sensor can then be determined using the width of the frame on the computer screen, which corresponds to the 6.20 [6] mm width of the sensor.  The magnification is given by:

               M = [ (Image width on screen) / (Frame width on screen) ] x 6.20 mm / (Object width)                        

All of the Macro photos were taken with no zoom, L format (4320 x 3240 pixels),  with the camera focused on the object.  The results of the calibration are given in the following table:



Table 1: Magnification and Calculated Resolutions vs Macro Distance (Equations 1-5 of [2] )

 Object

to

Barrel

mm

Magnif.

M

Lens

Res.

lp/mm

Sensor

Res.

lp/mm

Total

Res.

lp/mm

Object

Res

mm

 -4 @f/2.7  0.2329 593 348

300

0.014
 0  @f/2.7  0.1824 593 348 300 0.018 
 5  @f/2.7  0.1431 593  348 300 0.023 
 10 @f/2.7  0.1226 593 348 300 0.027 
 100 @f/2.7  0.0357 593  348 300 0.093
300  @f/2.7   0.0137 593 348 300 0.243
           
 0  @f/2.7  0.1824 593 348 300 0.018 
 0  @f/3.5  0.1824 457 348 277 0.020 
 0  @f/8.0  0.1824 200 348 173 0.032 


Note 1: For comparison, remember that the spacing of the filament coils being used as a test target was 0.024 mm (24 microns).
Note 2: Object-to-Barrel distance of -4 mm is for the object touching the lens, which is 4 mm behind the front of the lens barrel.  I normally try to avoid this, as a distance of 0 mm gives a resolution almost as good.
Note 3: For the SX30 f/2.7 gave the maximum detail, with slightly less at f/3.5.  At f/8 the detail was completely unresolved in the photo, as would be expected from Table 1.   I save my macro settings using Aperture Priority f/2.7.  This is best for resolution, for avoiding motion blur and for best low-light performance.  The only reason I can think of to use a smaller aperture (higher F-number) is when a larger depth-of-field is required.
Note 4: In [2], I reported a magnification of 0.1365 for an object 10 mm from the lens barrel.  The value of 0.1226 measured here is probably more accurate because of greater care in measuring the distances.

One thing to notice about Macro for the SX30 is that it is mainly the sensor that limits the resolution.  This can be seen from from the lens and sensor resolution columns.  The lens can resolve smaller angles than the sensor, with the result that the lens delivers most of what the sensor has to offer in the "total resolution" column.  This is the opposite of the findings for maximum optical zoom in [1], where the sensor can resolve smaller angles than the lens.  In that case, it is mainly lens diffraction that limits the resolution of the camera.

The views and opinions expressed in this article are those of the author and do not necessarily reflect the views and opinions held by dpreview.com or any affiliated companies.

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