I am using a smartphone for capturing photos and I need to estimate the camera sensor size (mm*mm). I have the resolution (in pixels) and the focal length (in pixels). I can also measure the size of any stationary object and its distance w.r.t the lens. Basically, I don't have a pixel-to-mm metric for any of the above parameters that I can use. Is there any way I can calculate that to estimate sensor size?
If you consider geometrical lenses, it is not possible to get sensor dimensions and focal length as an object only determines a certain angle and from that information you can only determine the sensor size/focal length ratio. E.g. you don't know which of the purple, orange or cyan case is inside the camera, and you get the very same picture.
You can try to use the non-geometrical quality of lenses, but that needs some understanding of the lens structure. E.g. you can play with large apertures, so that the DOF is small, measure the DOF and the camera distance, and calibrate the lens. Rather tedious task I guess, and I am not sure you would get the necessary precision.
If you know the actual focal length and can include the effective focal length of the lens in your model, you can calculate its crop factor, and estimate its size.
Taking my own camera as an example (it's what I know), I know I have a 50mm lens that is effectively a 75mm lens. For most camera phones you can search for these specifications online.
With this arrangement, you know that my sensor is 1.5 smaller than a full-frame 35mm sensor. Both my sensor and a full-frame sensor use the same aspect ratio, and full-frame is 36mmx24mm. That puts my own sensor at 24mmx16mm (36 / 1.5; 24 / 1.5).
If you can find the actual and effective focal length of your smartphone's camera lens, you can work out its crop factor in this way. For example, if its actual focal length is 4.1mm (as it is in the iPhone 5), and its effective focal length is 31mm (again, iPhone 5), we know the crop factor is (31 / 4.1) = 7.6. This would put the sensor size in the region of 4.7mm x 3.2mm, which isn't far off the actual spec: http://en.wikipedia.org/wiki/Image_sensor_format#Table_of_sensor_formats_and_sizes