Macro vs TeleMacro with SX30/40
Resolution Study of Macro vs TeleMacro for Canon SX30/40
This article was originally published August 6, 2012. First Revision August 27, 2012. Second Revision September 29, 2012. The purpose of this study is to examine how much resolution you get for Macro compared with TeleMacro. TeleMacro is simply telephoto at a relatively close distance so that Macro-like detail is obtained. Correction October 18/12: Sensor width was changed from 6.17 mm to 6.01 mm (see Reference 10). This made minor corrections to the magnifications and effective focal lengths in Table 1, and to the Sensor Resolutions, Total Resolutions and Object Resolutions in Table 2. Revision 3 - November 30, 2012: Sensor width was changed from 6.01mm to 6.20 mm (see Reference 10). This made minor corrections to the magnifications and effective focal lengths in Table 1, and to the Sensor Resolutions, Total Resolutions and Object Resolutions in Table 2.
Three cases are examined:
1. Macro f = 4.3 mm, f/2.7 with the object close to the lens (not examined by VisionLight )
2. Steen Bay's TeleMacro at f = 26.875 mm, f/4.5 (nominally 30 cm min focus distance) 
3. VisionLight's Case 1: f = 150.5 mm, f/5.8 (nominally 1.4 m minimum focus distance) 
- Sunny (some cloud)
- L format (14 MP on SX30) I found this to be especially important for Macro & TeleMacro. In all cases, M1 format (7 MP) gave less detail.
- ISO 80?
- Tripod with 2s timer
- Aperture priority mode (Av) set to lowest F-number.
- Test-Target: Reticle with 0.1 mm (100 micron) gradations.
Case 1: Macro: Don't use any zoom in Macro mode; f/2.7; test-target approx. 10 +/- 1 mm from front of lensbarrel, , which is 91 mm in front of mounting screw.
Entrance Pupil 70 mm in front of mounting screw. E = 10 + 91 - 70 = 31 mm
Magnification: M = (88.0/266.5)x6.20 mm / 15 mm = 0.1365
Effective Focal Length F = m x E = 4.23 mm
Case 2: AF focus. Zoom until aperture rises to f/4.5; keep zooming with min focus distance = 30 cm in EVF. When this changes to 40 cm, it is too far. Touch the zoom lever quickly to get back to 30 cm but just before the change to 40 cm. Focal length is not given in EVF so you can't get a precise value at the time of shooting, only later from EXIF data. I obtained nominal f = 25.5 mm, slightly less than Steen Bay . Test-target 12" (304.8 mm) from front of lens, which was 110 mm in front of the mounting screw.
Entrance Pupil 14 mm in front of mounting screw. E = 304.8 + 150 - 14 = 401 mm
Magnification: M = (46 pixels per mm of object) x (6.20 mm / 4320 pixels) = 0.0660
Effective Focal Length F = m xE = 26.47 mm
Case 3: AF focus. Zoom to 35x; Aperture changes to f/5.8. Test-target 50" (1270 mm) from front of lens, which was 130 mm in front of the mounting screw.
Entrance Pupil 710 mm behind mounting screw. E = 1270 + 130 + 710 = 2110 mm
Magnification: M = (49 pixels per mm of object) x (6.20 mm / 4320 pixels) = 0.0703
Effective Focal Length F = m xE = 148.3 mm
Table 1: Data for Resolution Calculations (Equations in Appendix)
|Case 1: 0.4" Macro||
|Case 2: 12" Tele||25.5||4.5||401||0.0660||26.47|
|Case 3: 50" Tele||150.5||5.8||2110||0.0703||148.3|
Table 2: Calculated Resolution (Equations in Appendix
|Case 1: 0.4" Macro||593||348||300||0.024||Sensor limits resolution|
|Case 2: 12" Tele||356||348||249||0.061||Lens & sensor equal|
|Case 3: 50" Tele||276||348||216||0.066||Lens diffraction limits|
Macro (Case 1) can resolve 24 microns on the target (line-pair separation), the 12-inch TeleMacro can resolve 61 microns and the 50-inch TeleMacro can resolve 66 microns. The following pictures show 100% crops of the 3 cases. The Macro (Case 1) has approximately double the pixels per mm of target as Cases 2 & 3. The pictures probably have to be downloaded to appreciate how much better Macro is than TeleMacro, but notice the scratches between 7 and 8 mm, which are barely visible in the TeleMacro.
Case 1: Macro 0.4" from front of lens Nominal f = 4.3 mm, f/2.7
Case 2: TeleMacro 12" from front of lens
Nominal f = 25.5 mm. f/4.5
Case 3: TeleMacro 50" from front of lens
Nominal f = 150.5 mm f/5.8
I took over a hundred pictures for these 3 cases, including flowers, human hair of approx 40 micron diameter and cotton fibres of approx 10 micron diameter. Even though the cotton fibres were not resolved (no distinct edges) by any of the 3 cases, they still had the appearance of being reasonably sharp but, when two fibres were parallel and closer together than a couple of diameters, they could not be resolved.
When there is a risk of losing your prey by using Macro, TeleMacro is a good option. There is little advantage to attempt getting within 1 foot (Case 2) because the resolution for the object at 50 inches in front of the lens (Case 3) is almost as good. Case 3 is also faster to accomplish: Simply zoom to 35x or more and back up from your target until the camera will focus at nominally 1.4 m, but actually around 50 inches, which is approximately 1.3 m.
Macro has approximately 2.7 times the resolution of TeleMacro. Just because TeleMacro is not as sharp as Macro, it does not mean that the photos cannot be impressive, even at distances more than 50 inches (1.3 m). Tele-Macro, which is really just telephoto with macro-like detail, is a great tool when you can't get close to your prey. The photo of this dragonfly (100% crop) is from 11 +/- 2 ft away from the camera at full optical zoom and 1.3x digital zoom. The back-hairs are not resolved (ie worse than 10% MTF) , and yet they still produce a pleasing effect in the photo:
|Dragonfly Distance 11 +/- 2 ft Full optical zoom + 1.3 X digital zoom|
 SX40 TeleMacro - Part 2 by VisionLight February 13, 2012 http://forums.dpreview.com/forums/readflat.asp?forum=1010&message=40604881&changemode=1
VisionLight considered 3 cases:
?a) SX40 at 150.5mm (840mm FF) at focusing distance of 4.5 feet from the plane of the sensor and gives a horizontal field of view of 3½ inchs.
?b) SX40 at 150.5mm plus 2.0 Digital TC (1680mm FF) at focusing distance of 4½ feet from the plane of the sensor and gives a horizontal field of view of 1¾ inchs.
c) SX40 at 150.5mm plus 4.0 Digital Zoom (3360mm FF) at focusing distance of 4½ feet from the plane of the sensor and gives a horizontal field of view of 7/8 inchs.??In response to Example 1, Steen Bay wrote: "It's also possible to get the same magnification at app. 150mm (equiv.), f/4.5 and 30cm distance, which probably would give a better result (more light, less shake and diffraction)." [ 150 mm equiv is an actual focal length of 26.875 mm ]
 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
 How to Properly Use the "Thin Lens Formula" to Model a 35 mm Camera `Thick' Lens, by Jerry Jongerius, Revision 7A, September 2, 2012, http://www.panohelp.com/thinlensformula.html
 Resolution of camera lenses where are the limits – and why?, Camera Lens News No. 2, fall 1997) http://www.dantestella.com/zeiss/resolution.html
 Spatial Frequency Response of Colour Image Sensors: Bayer Colour Filters and Foveon X3, Hubel et al: http://www.foveon.com/files/FrequencyResponse.pdf
 Sensor Resolution, Higgins, G.C.Appl. Opt. 3, v.1, 9, Jan 1964, http://www.diax.nl/pages/Lens_res_uk.html
 Introduction to Resolution and MTF Curves, Norman Koren, http://www.normankoren.com/Tutorials/MTF.html
 Measuring Lens Field of View (FOV) (aka: Locating the Lens Entrance Pupil), by Jerry Jongerius, http://www.panohelp.com/lensfov.html
 Panoramic photography - how to find the Nodal Point (no parallax point) of your lens: http://www.youtube.com/watch?v=k0HaRZi-FWs
 Canon Specifications for SX30 IS: http://www.canon.ca/inetCA/arcproducts?m=gp&pid=4812#_030 October 18, 2012 Revision: The specifications say there are approximately14.5 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. These numbers may be used in the calculation of magnification and sensor resolution.
November 30, 2012 Revision: 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: Resolution Measurements and Equations for Calculations
Reference 2 provides equations for resolution of distant objects at infinite zoom. The equations there are suitable for that case, but can be more generally applied to cases where the focus is not infinite if the lens focal length f in  is replaced with the effective focal length F, specifically in Equations 1b, 2b, 4a and 4b [Reference 3].
Reference  provides a table (from Zeiss) of resolutions for nearly-perfect lenses in line-pairs per mm as a function of F-number for a spectrum of white light. This table can be summarized by the following formula:
LensRes = 1600 / N (1)
??where LensRes is the lens resolution (approx 9% MTF) in line-pairs per mm (of the test-pattern image on the surface of the sensor) and N is the F-number. This equation is the same as Equation 1a of .
The resolution of the sensor, in line-pairs per mm, is given by:
SensorRes = 0.5 x Horizontal Pixel # / Sensor Width (2)
where Sensor Width is in mm. This equation is the same as Equation 2a of . This equation corresponds to the Nyquist frequency, beyond which spurious artifacts are created in photographs as a result of aliasing. At this frequency, the resolution of most real sensors is typically in the range of 4% MTF to 17% MTF for Bayer array sensors, rather than the theoretical 64% of an ideal monochromatic square-pixel array . I have therefore adopted Equation 2 as a very approximate representation of 9% MTF for the sensor.
The total resolution of the lens-sensor combination is worse than both of the two resolutions individually. It is given by:
TotalRes = squareroot [ 1 / ( 1 / LensRes^2 + 1 / SensorRes^2 ) ] (3)
where all of the resolutions are in line-pairs per mm. The symbol "^2" means that the quantity is squared. This equation is the same as Equation 3a of . The formula is attributed to Kodak . Some sources indicate that the exponent 2 in Equation 3 for total resolution is incorrect and that it should be 1, e.g. . I have chosen to retain the exponent 2, however, because an exponent of 1 yields resolutions that are far worse than my measurements for the Canon SX30 at full optical zoom, whereas the exponent 2 yields good agreement.
Image Magnification m is defined as:
m = ImageSize / ObjectSize (4)
One way to measure Imagesize is to measure the length of the image in a photo on the computer screen as well as the frame width. Knowing the actual width of the sensor, in millimetres, from the camera specifications, Imagesize = ( ImageLengthOnScreen / FrameWidthOnScreen ) x SensorWidth.
Conversion to Object Resolution
Object resolution (the minimum separation of resolvable details on the object) is most useful for describing the detail that can be captured in a Macro or TeleMacro photograph. The line-pair separation on the sensor is given in millimetres by (1 / TotalRes) from Equation 3. Dividing this by the image magnification m yields the line-pair separation in millimetres on the object. The object resolution is given by:
ObjectRes = 1 / ( m x TotalRes) (5)
Where ObjectRes is the object resolution in mm. If this is recorded to 3 decimal places, it is easy to multiply by 1000 to get the resolution in microns. ObjectRes is the line-pair separation on the object that can be resolved (9% MTF). Fine features, such as filaments and hairs may still give pleasing effects in photos, even when they have poorer than 9% MTF resolution. It is just that, when these fine features are close together and parallel, they blend together into a larger blurred mass.
Measuring the Location E of the Entrance Pupil and the Effective Focal Length F
The location of the entrance pupil and the effective focal length both depend, not only on the zoom of the camera, but also on the focus distance [3,8]. Reference 8 describes how to locate the entrance pupil by taking two pictures of an object at different distances, but using the same zoom and focus distance for both. The photo with the focus on the object may also be used to calculate the image magnification m. Reference 9 describes using the parallax method of locating the no-parallax point, which is another name for the location of the entrance pupil, commonly used in panoramic photography. For the SX30, I made a telescoping lever from a curtain-rod and bolted the camera to it in order to determine the location of the no-parallax point. The location of the entrance pupil is defined in  as:
E = Distance from object to the Entrance Pupil (6)
where E is measured in millimetres for a particular zoom setting and the camera's focus on the object. The measured angular resolution, in radians, may then be defined as the smallest resolvable line-pair separation on the target divided by E. (Multiply that by 1,000,000 to get microradians.)
The effective focal length is given by :
F = m x E (7)
where F and E are in millimetres. F is used in Equation 4 to calculate angular resolution. It is also used in the definition of F-number: N = f /D, where D is the diameter of the entrance pupil.
Conversion to Angular Resolution
Angular resolution is most useful for describing the resolution of distant objects. The total resolution in terms of line-pairs per mm on the sensor can be converted to angular resolution of the object from the the point of view of the entrance pupil. The angular resolution in microradians is given by:
TotalAngRes = 1,000,000 / ( F x TotalRes ) (8)
Where TotalAngRes is the angular resolution of the object in microradians
TotalRes is the line-pair per mm resolution on the sensor.
F is the effective focal length.
F is approximately equal to the lens focal length f only for infinite focus distance . In Equation 1, the F-number N is equal to F divided by D, the diameter of the exit pupil. In private correspondence with Jerry Jongerius of PanoHelp , he has confirmed that the entrance pupil diameter is the correct diameter to use for angular resolution calculations and that the resolution angles are to be measured from the location of the entrance pupil, even though both of these facts may seem counterintuitive. It seems especially strange in the case of the Canon SX30 at full optical zoom, where the entrance pupil is approximately a metre behind the camera, although the exact location varies somewhat with focusing distance.
Which Equations to Use
To summarize, if you want to calculate object resolution, use Equations 1-5 and it is necessary to measure the image magnification, which is a simple matter. If you want to measure angular resolution, you will need to determine the location of the entrance pupil, using Equation 6 to determine E. If you want to calculate angular resolution, you will also need to use Equations 7 and 8.
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