Yes, smaller sensors are more efficient

7

So here goes ...

I went over to DxO and selected three of the most recent and best-performing cameras in each of six size categories (while avoiding duplicates, i.e. cameras known or thought to have the same sensor). The cameras as well as the categories are listed in the table below.

I calculated efficiency in each of three ways: With regard to DR at ISO 100, with regard to DR at higher ISOs, and with regard to max SNR. I first calculated the statistic for each camera and then entered the average per size category in the table.

Normed ISO 100 DR: This is the unlogged DR at a DxO measured ISO of 100 divided by the sensor area. Before unlogging, the logged DR at ISO 100 was extra- or interpolated by the closest observations available using the following formula:

Logged DR at ISO 100 = BIDR + (LOG10(100) - LOG10(BI))*(BIDR - NIDR) / (LOG10(BI) - LOG10(NI))

where BIDR is the logged DR at the base measured ISO, NIDR the logged DR at the next measured ISO, BI is the base measured ISO, and NI is the next measured ISO.

Normed High ISO DR: This is the logged DR obtained for equivalent photos (same amount of total light on the sensor, same DoF, same shutter speed) at a higher measured ISO given by

12,800 * SA/864

where SA is the sensor area and 864 is the sensor area of real FF, i.e., 24 x 36 mm. The DR at that particular ISO was interpolated from the closest observations available using a formula similar to the one used for "normed ISO 100 DR".

Normed Max SNR: This is the unlogged max SNR normed by means of the following formula

Normed Max SNR = SQRT(BI) * SQRT(MP/8) * MSNR / SQRT(SA)

so as to constitute a measure of efficiency. MP is the megapixelcount of the sensor, 8 the megapixelcount used in DxO normalization, and MSNR the max unlogged and unnormed (i.e., per original pixel) SNR at base ISO.

My comments on the results:

All three measures increase in an almost perfectly monotonic fashion as we move from larger to smaller sensors with only minor deviations. These deviations can in most cases probably be attributed to differences in how recent the sensors are (the small PS cameras I could find at DxO are older than the large PS cameras, which are all new) or other pecularities of individual sensors in categories where there is not much to choose from (in the CX category, the RX100 II does very well whereas the Nikon 1 sensors are less impressive).

When it comes to "normed ISO 100 DR", the smallest sensors are more than two EV more efficient than their FF counterparts (i.e., the unlogged DR per area value is more than four times as large). For "normed high ISO DR" the corresponding difference is not quite as large but still more than one EV. For "normed max SNR", finally, the difference amounts to more than one EV extra exposure (SNR is expected to increase by the square root of two, i.e., 1.414, as you double exposure).

Further comments are welcome.