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Appendix  2

 

Calculation  of  the  approximate  width  and  area 

 

of  one  pixel  on  the  sensor  of  a  digital  camera

 

 

This appendix is part of  this article  about the “telephoto advantage” and "pixel density advantage" of an APS-C camera. This appendix has the following sections:

 

Calculation of pixel pitch

 

Calculation of the area of one pixel

 

Why is the pixel size and sensor size of a digital camera important? Does increasing pixel count increase noise? Big pixels vs small pixels.

 

(Click  here  to read the full article)

 

Pixel level vs image level in digital photography  (also refers to the  Studio Test Scene  published in September 2013 by Digital Photography Review)

 

Case study: High ISO low light images of the Sony A77 compared with those of the Sony A55

 

Downscaling and upscaling images for comparative purposes

 

Practical examples of the application of the "pixel density advantage" template

 

 

Calculation of pixel  pitch

 

In addition to  calculating pixel density, it can be informative to determine the approximate size of one pixel. It follows that, the greater the pixel density, the smaller each pixel becomes. The size of a pixel may be calculated using either a linear measurement or an area measurement.

 

A linear measurement of the approximate width of one pixel is known as the pixel pitch. The term  pixel pitch is defined  here  as “the center-to-center distance between individual pixels, in microns”.

 

Note: This is a very complex subject because, for example, there can be gaps between individual pixels. Therefore, the measurement of "pixel pitch" may not provide the "true" width of one pixel. Note that this article does not discuss the various complex issues that can arise when estimating the width or area of individual pixels. It is recommended that you study a detailed technical article if you would like to become familiar with these issues. For example, you may find this  DPR forum discussion  about pixel density and pixel pitch to be helpful. Therefore, the calculations set out below are presented only for the purpose of calculating the approximate width and area of one pixel, and for illustrating the mathematical relationships between pixel size, pixel density, and image size. 

 

In practice, the following formula has been used to calculate pixel pitch:

 

Pixel pitch = width of sensor in mm  divided by   image width in pixels

 

We shall now demonstrate how this formula can be applied to our camera specifications for FF and APS, as set out earlier in  Practical Example "B", that is, we shall assume that the sensor sizes and image dimensions of our two "theoretical" cameras are as follows:

 

Camera “FF” has a “full frame” sensor, which measures 36mm x 24mm. FF produces a maximum image size of 6000 pixels x 4000 pixels, and is therefore a 24 megapixel camera (6000 pixels x 4000 pixels gives an overall image area of 24 megapixels).

 

Camera "APS", is an APS-C camera, which has a sensor that measures 24mm x 16mm. APS produces a maximum image size of 4800 pixels x 3200 pixels, and is therefore a 15.36 megapixel camera.

 

Therefore, the calculations are as follows:

 

Pixel pitch = width of sensor in mm  divided by   image width in pixels

 

Pixel pitch for FF  =   .006 mm   (36mm sensor width  / 6000 pixels image width)

 

Pixel pitch for APS = .005 mm   (24mm sensor width / 4800 pixels image width)  

 

Note that, instead of expressing the above answers in millimetres, they are often expressed in “microns”. A “micron” is also referred to as a “micrometer”, and it is a unit of length which is one-millionth the size of one metre. Therefore, there are 10,000 microns in 1 centimetre (cm), or 1000 microns in 1 millimetre (mm). Further information about microns can be obtained  here. Note that the symbol for “micron” is µm.

 

Therefore, to be expressed in microns, the above results need to be multiplied by 1,000. This gives the following answers:

 

Pixel pitch for FF =    6 microns   (.006 mm x 1000)

 

Pixel pitch for APS = 5 microns   (.005 mm x 1000)

 

So, in this example, the pixel pitch of FF is 20% greater than that of APS  (6 / 5).

 

This reconciles with the 20% “gain in image width” that is calculated  hereIn addition, the pixel density (in pixels per linear centimetre) of APS is 20% greater than that of FF  (2000 / 1666.67). The pixel density for this example is calculated  here.

 

 

Calculation of the area of one pixel

 

The area of one pixel may be calculated by squaring the pixel pitch.

 

Area of one pixel of FF  =   36 square microns   (6 microns x 6 microns)

 

Area of one pixel of APS = 25 square microns   (5 microns x 5 microns)

 

So, in this example, the area of one pixel of FF is 44% greater than that of APS  (36 / 25).

 

This reconciles with the pixel count (expressed in megapixels) of the full sized image of APS, which is 44% greater than the pixel count of the cropped image of FF (15.36 megapixels / 10.67 megapixels). In addition, as calculated  here, the pixel density (in megapixels per square centimetre) of APS, is 44% larger than that of FF (4 / 2.778).

 

Note: The area of one pixel can also be calculated as follows:

 

Area of one pixel in square microns = area of sensor in square microns  divided by  the number of pixels on the sensor

 

Using this formula, the calculations are:

 

Area of one pixel of FF =    36 square microns  (864,000,000 / 24,000,000)

 

Area of one pixel of APS = 25 square microns  (384,000,000 / 15,360,000)

 

Note that  Appendix 1  shows the image size and pixel density calculations based on  area  measurements.

 

It is important to study  Appendix 3  because this appendix provides a very valuable summary of the mathematical relationships between image size, pixel density, and pixel size, based on the example and calculations we have provided above. The information in Appendix 3 can be used as a template for calculating the pixel density and pixel size of any camera that has a 3:2 aspect ratio.

 

 

Why  is  the  pixel  size  and  sensor size of  a digital  camera  important?

 

Does  increasing  pixel  count  increase  noise? 

 

Big  pixels  vs  small  pixels

 

 

The purpose of this literature review is to provide links to articles on internet that discuss the topic of why the pixel size and / or sensor size of a digital camera are important considerations for buyers of digital cameras.

There is considerable debate amongst photographers about whether increasing the pixel count on the sensor of a digital camera will lead to increased noise at the  image level, particularly when images are recorded in low light and require a relatively high ISO setting. However, there appears to be little doubt that increasing the pixel count leads to increased noise at the  pixel level.

The sensor type and size are also important factors, as explained, for example,  here  and  here. The following is a brief literature review of some of the material on internet that deals with these issues.

 

Statement from Sony designers about the high pixel count of the 20.2mp Sony RX100

 It is interesting to read some material published by Sony when, in 2012, the 20.2 megapixel Sony RX100 came on the market.

Here is an extract from a posting made in 2012 on the  DPR Sony Alpha SLR / SLT Talk Forum:

"I think that when most cautious people are investigating whether or not to purchase a new camera that has a higher pixel count than the one they currently use, they want to ensure that the high ISO performance of the new camera is at least as good as that of the lower megapixel camera they are currently using. I don't think this is being unrealistic!

"Sony is very sensitive to the fact that many photographers appreciate the fact that increasing the pixel count increases noise and that they want reassurance that the new higher megapixel sensors have adequately dealt with this problem. Consider, for example, this statement from Sony about the high pixel count of the new Sony RX100:

Question to Sony:

"Why did you want a 20.2-megapixel sensor? I heard that this incredibly high pixel count would negatively impact noise levels, thereby decreasing image quality at high ISO settings.

Answer from Sony:

Ueda (Image Quality Design)

"It’s true that increasing pixel count increases noise. But since we manufacture our own sensors, we can easily tweak sensor specs to suit specific needs. This allowed us to craft a totally new sensor that delivers superbly detailed images with low noise. For high-sensitivity shooting we managed to reduce noise levels below those of existing Cyber-shots by combining technologies from Cyber-shot and α Series. As a result, we can shoot at up to ISO 6400 for normal photos and up to ISO 25600 when using Multi Frame NR."

http://www.sony.com.sg/microsite/cybershot/rx100/pdf/performance.pdf

This matter was also discussed further in  this DPR forum posting:

"Also in the above statement, Kaimi (Product Design) said this:

"Some compact cameras keep noise down with lower pixel counts. But there are users who really want super-fine images, which require a high pixel count. But if the higher pixel count leads to unacceptable noise levels that the noise reduction system can’t reduce without affecting image quality, it is essentially self-defeating. Our new sensor achieves both super-fine images and low noise so even distant landscapes shot at telephoto focal lengths show great detail. People are going to love this compact camera for travel photography."

The above is only part of the literature review. Click here to read the full article, which includes the views of Sony engineers, Dr. Eric Fossum, Dr Bob Atkins, Dr. Roger Clarke, Peter van den Hamer, Cambridge in Colour, Joseph James, Emil Martinec and more.

 

Pixel level vs image level in digital photography

It is sometimes suggested on photography forums that, although increasing the pixel count may result in increased noise, this may be visible only when an image is "pixel peeped". Remember that digital images can be examined at either a "pixel level" or an "image level". When an image is examined at a "pixel level", or at a 1:1 or 100% magnification (or greater), any defects in the image can be seen more clearly than when a much smaller sized image is examined. Note that, examining an image at 100% magnification (or greater) is sometimes referred to as "pixel peeping". To obtain a range of views on how the term "pixel peeping" should be interpreted, you could read this “Digital Photography Review” (DPR) discussion thread:

 

Please define "pixel peeping": May 2013: Digital Photography Review, "Beginners Questions Forum".

 

The "Digital Photography Review Studio Shot Comparison Tool  enables users to select from a wide range of cameras and exposure settings and then highlight a very small part of the image to compare the image quality of the selected cameras. For example, try comparing the RAW image quality of the full frame Sony SLT-A99 at ISO 3200 with that of the APS-C Sony SLT-A77. It is over to the photographer to decide whether the considerably increased noise visible in the Sony A77 image at the pixel level would also be visible at the image level! Note that a comparison of the pixel sizes of the Sony A99 and the Sony A77 can be seen  here.

 

Although the pixel pitch of the Sony A99 is about 52% greater than that of the Sony A77, this may not be the only reason why high ISO images from the Sony A99 are better than those from the Sony A77. The A99 has a full frame sensor, but the A77 has a smaller APS-C sensor, so the larger sensor of the A99 is also likely to help the A99 produce better high ISO / low light images than can be obtained from the A77.

 

In September 2013, the DPR introduced its new  Studio Test Scene. Note that the reasons why the DPR introduced a new digital camera comparison tool are discussed  here. This excellent studio scene comparison tool enables the user to compare the cameras' full image sizes or to select the option to 'normalize' the scene to a standard print size or social media size. In addition, the user may select either a daylight or low light simulation.

 

To further add to its usefulness, the DPR has even included the  80mp Phase One IQ180  camera as a reference camera for its Studio Test Scene. It is very revealing to use the "full image size" option to compare, for example, the detail captured by a 16mp camera with that captured by the 80mp Phase One IQ180.  You will notice a huge difference when the 80mp image is "normalized" for comparison with a 16mp image from, say, the Sony A57. Some of the very fine detail in the 80mp image almost disappears (such as the name "Carl Ritter" on the bank note). This can be a disadvantage of downscaling one image for comparison with another image (as discussed below).

 

Note that the sensor size of the  Sony A57  is 23.5mm x 15.6mm, but the  Phase One IQ180  has a sensor size of 53.7mm x 40.4mm. So, it's likely that the much larger sensor size and number of megapixels of the IQ180, both have a significant part to play in the big improvement in image quality of the IQ180 when compared with that of the A57. Examples of the "sheer resolving power" of the medium format IQ180 in images taken at Queenstown, New Zealand, can be seen  hereThere is also an interesting article  here  about why a photographer moved to the medium format provided by the 40 megapixel Phase One IQ140 camera.

 

It is difficult to find a definition of the term  "image level"  that has been agreed on by a majority of photographers! However, my opinion is that, viewing an image at the image level could be interpreted to mean that the photographer views the whole image rather than just a 100% magnification of a small part of the image. For example, if a large print has been made of an image (say 40 inches wide), the photographer may stand back one metre (or more) from the print and may not, therefore, notice small defects in the print that might be noticeable if a small section of the print was examined with a magnifying glass at very close range!

 

Note that, when an image has been downscaled and printed (or displayed on a screen) at a relatively small size, any defects in the image will become much less visible compared to what can be seen when the same image has been printed (or displayed on a screen) at the largest practical size! Therefore, when comparing an image at both the pixel level and the image level, my approach is to ensure that the image level examination is made on a full-sized image that is printed (or displayed on a screen) at the maximum size that can be obtained without degrading the image quality in any way. A discussion on how to determine the maximum acceptable print size for an image can be seen  here.

 

Note that, an image level examination may be made on images that have been downscaled and printed (or displayed on a screen) at a relatively small size. However, it would not be fair to then claim that defects, noise, (or fine detail) in such downscaled images can be seen only when they are viewed at the pixel level!

 

For example, have a look at both the images that are displayed  here. The first image on the page has been downscaled from its full size of 6048 pixels x 4032 pixels, to a web viewing size of 870 pixels x 572 pixels. However, the second image on the page, which shows just a small part of the image, has not been downscaled at all. Note how much extra detail can be seen in the second image in comparison with what can be seen in the first image, such as the name on the boat and the rails around the boat. Therefore, in this example, I would make my image level examination based on looking at the full-sized image at the level of magnification shown in the  second  image.

 

On 30 August 2011, Yasuhiro Ueda of Sony's Image Sensor Business Division, Semi Conductor Business Group, issued a semiconductor briefing "Image Sensor Business". As part of this briefing, a diagram was produced titled  "Misconception that reduced pixel size causes deterioration in characteristics". This diagram has sometimes been reproduced on  forums  to support the view that reducing the pixel size does not necessarily lead to a noticeable deterioration in image quality when the image is viewed at the image level.

 

Incidentally, the topic of why “DXOmark” tests dynamic range on an image level, was discussed in March / April 2012 in this DPR thread:

 

DxOmark: pixel level vs image level DR

 

 

Case Study: High ISO low light images of the Sony A77 compared with those of the Sony A55

 

On 25 October 2011, the  "Digital Photography Review"  (DPR) published its in-depth review of the 24 megapixel APS-C Sony SLT-A77. This review included a separate page to compare the high ISO RAW noise of the Sony A77 with that of the 16 megapixel APS-C Sony SLT-A55. This page can be seen  here.

 

Note that the pixel pitch of the Sony A55 is about 4.8 microns compared with about 3.9 microns for the Sony A77. Therefore, some photographers were concerned that, because the Sony A77  pixels are smaller  than those of the Sony A55, the high ISO, low light performance of the Sony A77 might not be as good as that of the Sony A55. Note that the sensor size of both the Sony A55 and the Sony A77 is about 23.5mm x 15.6mm.

 

 The DPR comparison (referred to above) said that:

 

"What we want to know here is whether - if you're used to the output from the A55 - the A77 will give you substantially different image quality when you use the files in the same way."

 

The  first set  of DPR images on  this page  show how the A77's raw files look at 100% next to those captured by the A55 at the same ISO setting of 12800. The DPR concluded that:

 

"It is evident from these images that the A77's pixel-level noise is slightly higher, on visual inspection, than the A55, but not by much. Both chroma and luminance noise are more intense, but after default levels of noise reduction are applied in ACR, the difference is not of much practical significance."

 

The DPR then presented a  second set  of images in which the A77's 24mp files were downsampled to 16mp to match the output resolution of the A55. The DPR said that: 

 

"The purpose of doing this is to establish whether the A77 is a noisier camera than the previous-generation A55 when its greater pixel count is taken out of the equation."

 

The DPR concluded that:

 

"Even when its files are downsampled to 16MP, images the A77's 24MP sensor still display slightly higher noise levels at ISO 12800 than the 16MP sensor of the A55, as you can see from the images above with noise reduction turned off."

 

The above case study shows two different ways in which 16mp images can be compared with 24mp images. Note that the quotations provided above give only a brief summary of the comparisons made and the conclusions reached by DPR, so it is recommended that you read the whole report. It may be concluded that,  if  the 24mp A77’s files are  downsampled  to 16mp, then the noise levels in low light, high ISO situations, are very similar to those of the 16mp A55.

 

In December 2013, this topic was discussed  in this DPR forum posting. The posting linked to is headed "Sony A57 vs A77: Proof that pixel count affects noise".

 

 

 Downscaling and upscaling images for comparative purposes  (can apples be compared with oranges?)

 

If the  prime objective  of a comparative test is, say, to observe the amount of detail captured in  bright light  by a 24mp APS-C camera, in comparison with that captured by a 16mp APS-C camera, my personal preference is  not  to downsample the 24mp image, because this can reduce the amount of detail recorded in this image.

 

In these circumstances, I would prefer instead, to compare prints made from full-sized images from both cameras printed consistently at  the same pixels per inch. If, for example, the images from both cameras are printed at 150 pixels per inch, then the print size from the 16mp camera is 32.75 inches x 21.76 inches (from a file size of 4912 x 3264 pixels) and the print size from the 24mp camera is 40 inches x 26.67 inches (from a file size of 6000 pixels x 4000 pixels).

 

One of the reasons why a photographer may purchase a 24mp APS-C camera in preference to a 16mp APS-C camera, is that there is an expectation that a full-sized image from the 24mp camera may exhibit more detail than a full-sized image from the 16mp camera! So, if I habitually make prints at 150 pixels per inch from images from a 16mp camera, I would also like to print my images from a 24mp camera using the same 150 pixels per inch. In these circumstances, I would obtain a print size of 32.75 inches x 21.76 inches from the 16mp camera, and 40 inches x 26.67 inches from the 24mp camera.

 

Although in this comparison the print sizes are not equal, nevertheless, I would find it very useful and informative to compare the two prints side by side to see whether the print from the 24mp image exhibits more detail than the print from the 16mp image. Now, some photographers have insisted that this comparison is like  "comparing apples with oranges”  because the print sizes are not equal. However, it is also inconsistent to downscale the 24mp image and not the 16mp image, when the prime objective (as stated above) of the comparative test is to compare the amount of detail captured in bright light by both the cameras. It is also inconsistent if the comparative images are not printed using the same pixels per inch.

 

Another alternative is to upscale the 16mp image to 24mp, rather than downscaling the 24mp image to 16mp. Although this will result in obtaining prints of equal size, it could be argued that it is inconsistent to upscale one image and not the other, when comparisons of the amount of detail captured are being made. Note that this topic has often been debated on camera forums, such as  this thread about upscaling vs downscaling.

 

In practice, when comparing images from sensors with different pixel counts, it may be a good idea to use several of the methods referred to above and see whether a consistent pattern of results emerges!

 

Can apples be compared with oranges?

 

One interesting project would be to make a comparison of digital images that demonstrates the huge advances that have been made since the Year 2000 in the quality and size of digital images.  

 

For example, we could compare an image captured by one of the first 3mp consumer digital cameras (say manufactured in the Year 2000) with an image captured by a 24mp recent digital camera. Both images would need, for example, to be taken at the same time, and record the same scene with the same lighting and the same field of view.

 

When  both images  are consistently printed at 150 pixels per inch, the print from the 3mp image would measure about 14.1 inches x 9.4 inches, compared with about 40 inches x 26.67 inches from the 24mp image.

 

Now, if the 24mp image is  not  downscaled, the resulting 40-inch wide pride print is likely, for example, to exhibit a great deal more detail than the 14.1-inch wide print from the 3mp image. I would like to see two such prints, side by side in an exhibition, with the purpose of demonstrating the huge amount of progress that has been made with digital camera technology since the Year 2000!

 

Of course, it could be argued that it's simply "not fair" to compare images from a recent 24mp camera (using a superb recent lens) with images from an "ancient" 3mp camera (using a much inferior lens). In other words, this would involve "comparing apples with oranges".  But, as shown in  this article  "it is not difficult to demonstrate that apples and oranges can, in fact, be compared"!  And, of course, the way in which comparisons are made, and the validity of such comparisons, depends entirely on the  prime objectives of the comparisons.

 

Therefore, if the  clearly stated pime objective  of the comparison is to demonstrate the huge advances that have been made since the Year 2000 in the quality and size of digital images, then it could be argued that it is reasonable to compare the "ancient" 14.1-inch wide print with the "recent" 40-inch wide print. Of course, if the results of such a comparison are published or displayed, the prime objective of the comparison, the major differences between the equipment used, and any exposure differences in the images being compared, should be clearly stated!

 

As mentioned above, it is very revealing to use the "full image size" option in the new DPR  Studio Test Scene  to compare, for example, the detail captured by a 16mp camera with that captured by the  80mp Phase One IQ180  camera. If printed at 150 pixels per inch, an image from a 16mp camera would provide a print width of about 33 inches compared with a print width of about 69 inches from an 80mp image. However, the comparable print width for an image from a Year 2000 3mp camera is only about 14 inches!    

 

Even if a 3mp image is upscaled to a 24mp image, the upscaled image is likely to "pixelate" and this process cannot create any additional detail that was not captured at the time the 3mp image was taken. Conversely, even if the 24mp image is downscaled to a 3mp image, the downscaled image may still show more detail than the unscaled "ancient" 3mp image.

 

 

 

Practical examples of the application of the

"pixel density advantage" template

 

Click  here  to see the practical examples of the application of the "pixel density advantage" template.   

Click  here  to go to the index of all the technical articles and blogs by Rob's Photography.

 Amazing image quality of images captured using the Sony Zeiss FE 55mm F/1.8 lens on the full frame 42.4mp Sony A7RII: This page includes a selection of images that demonstrate the excellent image quality and amazing detail that can be captured using this lens. To give you an appreciation of how these images will appear when greatly enlarged, crops of just small areas of the images are included, or the full-sized image is published. A similar page that shows the excellent clarity of selected Sony A99 and A900 images can be seen  here.