Ever wondered what the maximum printed enlargement would be without up-sampling the image? Or, you are shopping for a new camera and want the camera to deliver an image that can be enlarged to your maximum printer capability without loosing detail due to up-sampling?

Today, digital cameras come with a variety of sensor sizes and resolutions and printers are available to complement them. There are many of them! This article is mainly directed to the "prosumer" however, applicable to any and all digital cameras buyers.

Camera sensor resolution has gone from 4 MP to 22 MP with sensors from 4mm x 3mm  to 36mm x 24mm (standard 35mm). Examples in this article are based on the APS-C-C Canon 20D  (22.5mm x 15 mm)  sensor. 

Most camera manufacturers specify the sensor size in either MM or inches and total resolution in pixels. Only few list sensor-width/height-resolution (SWr and SHr) or maximum file size. For instance, the sensor of the Canon 20D has a listed resolution (SWr) of 3504 Pixels. The maximum print size without up-sampling would be:

Print width dimension = sensor-width-resolution divided by print-dot or pixels per inch (SWr / DPI) and print short dimension = sensor-height-resolution divided by print dots or pixels per inch (SHr / DPI),  or using actual numbers, 3504 / 240 = 14.6 inch and 2336 / 240 = 9.7 inch, rounded-off to 10 x 15 print.

Up-sampling the image 10 to 25% using a photo editor would increase the print size to a maximum of 18 x 12 inches. Up-sampling* more then 25% would result in to much loss of detail and probably destroy the print.

Now suppose you are shopping for a new camera and your criteria is the ability to print a 13 x 19 un-sampled* print @ 240 DPI. Any good image editor will tell you that a 13 x 19 print @ 240 DPI is 4560 x 3120 Pixels equals 14.228 MP. therefore, you need to look at camera's that have at least a 14 MP sensor.

If the maximum file size (sensor width/height resolutions) is listed among the sensor specifications, just divide the corresponding print size dimension to obtain the maximum sensor deliverable DPI. As an example, using the same example camera as above with an 8.2 Mp sensor and a maximum resolution of 3504 x 2336 Pixels (8,185,344  MP). Simply divide the SWr by the desired print size as follows;  3504 / 19 = 184 DPI. This is 56 DPI short of the desired thus, the need for a sensor with more pixels is obvious but how much more? This can be solved with a simple ratio like 240 DPI over 184 DPI, SR over 8.2MP = 10.6 MP** where SR = sensor resolution needed. Now, you are looking for a camera with a sensor resolution between 10.6MP and 12MP.

The New Sensors

Recently  Canon came out with two new cameras. One, the 5D has a 22,100,000 million/pixels full size sensor the other,  50D has an 15,200,000 m/pixels APS-C sensor.

To demonstrate how important sensor/size/ pixels become when the objective is to make the best possible large print consider the following when comparing sensor area in mm² versus print area mm² versus consequent pixels.

• The area of an APS-C sensor is  22.5 x 15 mm = 337.5 mm²
• The Area of an 35 mm sensor is 16 x 24 = 855 mm²

That is a ratio of 2.5  (855 divided by 337 = 2.5)

From above, we like to make a 13 x 19 print. The area of an 13 x 19 print in mm is;

13" x 25 = 325 mm and 19" x 25 = 475 mm. The print area therefore is 325 x 475 = 154,375 mm².

To make an 19" print using a camera with an APS-C sensor we have to enlarge the sensor area 457 times (154,375 print area divided by 337.5 sensor area = 457 times.)

To make the same print using a full size sensor the sensor multiplication is 180 times,  (154,375 print area divided by 885 sensor area = 180 times or a 1 to 2.5 difference ratio)

The sensor area pixels (15,200,000 MP APS-C) are enlarged over the larger print area and the resolution therefore can be calculated as follows; 15,200,000 divided by 154,375 mm² = 98.5 pixels per mm² or 98.5 pixels x 2.5 = 246 pixels per linear inch. That is just right to make a nice 13 x 19 inch print.

By the same token. the 35 mm full size ( 22,100,000 MP) sensor is capable of delivering a much higher resolution. It calculate as follows; 22,100,000 divided by 154,375 mm² = 143 pixels per mm² or 143 pixels x 2.5 = 358 pixels per linear inch. That is a higher resolution than needed  to make a nice 13 x 19 inch print based on the industry 240 DPI standard. But for interest sake, we could make a print 2.5 times larger (without up-sampling) using a  35 mm sensor then with an APS-C sensor. For the sake of argument that would be the square root of (13 x 19) x 2.5 = 24 or 18 x 24 inch print.

So, to make a technical optimal 24 inch print without up-sampling, one needs a full size sensor however, to cheat the technical correct, I have made many near perfect prints up-sampling the image 1.25 and higher ratio s using Adobe Photoshop software. This exercise also says, if you can afford it, go for the big one!

The above examples are applicable to any requirement by substituting the example values with required data.

Variables, nomenclature and example information.

• * Up-sampling is an invention of Photoshop meaning adding pixels selectively to thee image to make a print larger. See Photoshop manual for further details.

• ** Ratio caculation means having 3 values and calculate the fourth like; Alarge/Asmall   Xlarge/Bsmall where A = known common items large & small, B = known other lesser value, X = unknown larger value calculated by cross multiplying Alarge x Bsmall dividing the result by Asmall to obtain Xlarge.

• SR = sensor resolution,   SW = sensor width,   SH = sensor height,   SAr = sensor area resolution in square units,  SWr = sensor width resolution ,   SHr = sensor height resolution,  Maximum enlargement = SWr / DPI and SHr / DPI

• Example sensor size = APS-C-C (22.5 x 15 mm or 0.877 x 0.585 inch),   Example sensor resolution = 8.2 MP,   Example printing resolution = 240 DPI considered the minimum printing resolution where 360 DPI is the preferred professional printing resolution.