Exposure meter basics

The introduction of the Leica M-A that has no exposure meter, obliges the user of this camera to review the art and technique of hand-held exposure metering. The basics of exposure metering are quite simple, and modern digital cameras have effective metering systems combined with a wide dynamic range, making the goal of a properly exposed image most often a mindless exercise.What happened is this:analysts at the big camera manufacturers during the 1990s studied large amounts of pictures to get to know what pictures people take and  what the typical brightness distributions are for a number of subjects. A dark center area with a bright ring around it, was assumed to be a portrait with backlight or a black dressed person in the snow, depending on the relative size of the brightness areas. A darker area in the lower part of the picture and a brighter upper part was assumed to be a landscape. Quite sophisticated patterns were catalogued and put in a database. The matrix grid of the in-camera exposure meter (from 5 to 1004 different cells) recorded a certain pattern and searched in the database to find a pattern that matched as close as possible. The exposure could then be adjusted according to the preferences of the camera maker.
The emulsion makers did something comparable in the 1930s. The film emulsions needed a minimum amount of light to become developable and there was a maximum amount of light to blacken the emulsion completely. Analysing common scenes and measuring the maximum brightness differences in a scene produced the insight that on average a scene has a brightness range of 1:160 or 7.3 stops. The once popular Weston Master meter used a range of 1:128 with a highlight subrange of 1:8 and a shadow subrange of 1:16. In aperture terms there is a shadow range of four stops and a highlight range of three stops when you expose for the average. This range is almost identical to the famous Zone System range around the average value of Zone V: the darkest zone is Zone I (four stops in the shadow range) and the brightest zone is Zone VIII (three stops in the highlight range). 
Film emulsion makers produced characteristic curves for their emulsions that could accommodate these seven stops, provided the exposure meter gave an exposure that would peg the measured value somewhere in the neighborhood of the middle of the characteristic curve. See red dot in picture below.
A more precise indication is this: every exposure meter is calibrated to assume that the measured value represents a reflection of 17.68% of the light falling on the measured scene. This value corresponds with a density of 0.75 on the negative.Film emulsions, after proper exposure and proper development have a density range from fully transparent to fully opaque or in density values from 0.00 to 3.0. The useful range lies between 0.2 (dark shadow) and 1.5 (specular highlight). The  density of 0.65 to 0.75 lies somewhere between these endpoints. This is the theory behind the Zone System calibration: take a reading of the light reflected from a grey card with your exposure meter, preferably an handheld one. If everything is OK, the density of the negative has be around D=0.75 or with modern thin layer films D=0.55 to D= 0.60. Develop the film and see if the exposed negative has the required density. If OK, be happy, if not OK adjust ISO values and/or development times, within the  usual margins: characteristic curve not to steep, shadow density  (the four stops under exposure) around D=0.1. 
The exposure meter is simply a measurement instrument. It measures the total amount of the reflected light falling on the sensor of the meter. There is no trick here. The scene is composed of patches of brightness, whose size and intensity differ. A large black area can be adjacent to a very small white area. The integration process adds the intensity of the amount of energy reflected from the black patch to the amount of energy  reflected from the white spot and adjusts this value to the reference value of the grey card. The energy of the reflected light is measured in candela per square meter. Assume now for the sake of the argument that is has been established that a film with a speed of ISO 100 needs an exposure of 100 cd/m^2 to produce a density of 0.75 when developed under standardized conditions. The meter reads a value of 50 cd/m^2, but needs a value of 100: so the meter will adjust the exposure to get this value: in this case one stop more exposure: the black patch will be a shade of grey on the negative. This is how all Leica exposure meters for the M3 to M4-P (Metrawatt) and the internal metering in the M6 to MP and M8 to MM work. There is some adjustment, because the meter will give a higher priority to the  light falling on the center spot of the meter area. The exception is the multi-field metering on the sensor of the M camera. But even in this case there is only one final exposure value. The program adjusts the meter reading according to some pre-defined algorithm, like “neglect the value of the top right area” or “reduce the value of the middle area by 25%”, depending on the analysis of the comparison of the brightness values of the five fields.

The exposure meter fully neglects the ideas and intentions of the photographer. The small bright area in the scene will not influence the metering values much, but this area might be very important for the photographer and should be valued more by the selected exposure.The simplest method is the use of a handheld exposure meter that can read incident light. The procedure is easy to follow. Use the diffuser of the exposure meter and measure the light falling on the subject. There is no need to be close in front of the subject as long as the exposure meter can do a substitute reading that captures the same amount of light. This reading will give you the exact value for the grey card reading and neglects the brightness distribution of the scene. You can then analyze the scene and decide which part is the most important and adjust the reading to reflect this selection. If you do not wish to do this analysis, you can use the classical Duplex method that is foolproof: (1) select the flat-receptor position of the meter (both the Digisky and the L-478 have this option) (2) measure the incident light falling on the scene while holding the meter in the direction of the camera standpoint and (2) measure the incident light with the meter positioned towards the  main light source (most often the sun) and let the meter average  both readings. 
The new Leica M-A (basically a resurrection of the M4-P with design elements from the M3) may revive the interest in manual handheld exposure metering and the basics of film development and printing.
The theory behind the calibration of the exposure meter and the film emulsion sensitivity is explained in my book: Leica Practicum. 

Exposure meter and sensitivity

There are many discussions and reports floating in cyberspace that note that there is a discrepancy between the meter readings of the Leica M9/M8 and classical exposure meters like Sekonic or Gossen.Let us go to the basics to understand why this is the case.Silver-halide emulsions used in cameras are transparent after development and show a range of density differences from blank or fully transparent (no exposure = no light falling on the film) to black or fully opaque (maximum amount of exposure). When the maximum density has been reached more light falling on the film will not increase the density: this is the saturation level.
Exposure = illuminance x time
Density = log (10) Opacity (= 1/transmittance).
Photographic speed in ISO values is defined as the exposure required to to produce a certain density with recommended processing. You need a constant to compensate for additional influences. Therefore the formula for speed is (simplified): S = k/H
k= constant and H = exposure in metre-candle-seconds to produce a density of 0.1 above fog. This definition of speed refers to the minimum amount of exposure to record a weak signal.
For a ISO 100 film-speed this amounts to 0.1 lux-seconds.
For the determination of the exposure for a real scene a handheld exposure meter can be used. Every manufacturer of an exposure meter has a calibration formula to ensure that the measured exposure value (time + aperture) of the light intensity produces a certain density on the film (in most cases the famous middle grey density.
The standard calibration formula for reflected light measurement is
Illuminance = Constant x (Aperture)^2 x (number representing ISO-speed) / (exposure time) x pi.
Handheld exposure meters are calibrated according to strict rules to ensure compatibility, but Japanese meters and German meters employ slightly different values for the Constant. Therefore under identical circumstances the indicated exposure may differ by a quarter to a half stop.
In-camera exposure meters are calibrated according to the makers best ideas about what constitutes a perfect exposure. Measured at the film plane the correct exposure can be determined by the following formula:
IxT = C/S
I = illuminance in lux
T = exposure time in seconds
C = Constant = 10 for lux or 0.8 for foot-candles
S = ISO speed
The formulas are presented here as a guide to inform the reader that there are many influencing factors that determine the exposure and that there is much room for different interpretations what constitutes the perfect exposure.
The formula mentioned above (S = k/H) is still valid for digital systems, but k = 10.
Slide film as example uses a fully different method to determine ISO speed. Slide film cannot be overexposed because washed out highlights cannot be recovered. That being the case experienced slide film users have their metering method adapted to the material and the shaded of white they want to be visible in the slide.
Seasoned black-and-white photographers often use the Zone System to calibrate their equipment.

Modern digital sensors follow the same basic rules for exposure determination. There are however significant differences. The most fundamental difference is the fact that sensor surfaces are not transparent and therefore all methods that are dependent on reflectance and transparency do not work. The sensitivity of a photo detector (CCD or CMOS) is represented as the ratio of an output signal level to a received illuminance level. Here ‘output level’ is for digital systems what ‘density’ is for silver-halide systems.

The definition of a correct exposure cannot be related to the minimum density because that makes no sense in digital systems. But the standards still require that the speed of a digital sensor should be determined such that ISO 100 still refers to an average illumination of 0.1 lux-seconds.
For practical reasons the determination of the exposure at the sensor surface of a digital camera (like the M8/9) can be made according to four different methods. Any manufacturer may choose whatever the engineers think is best.
(1) ISO saturation speed is the S value when the exposure level generates a picture with image highlights that are just below the maximum possible (saturation) camera signal value (see the slide film discussion). The specific tone curve of the sensor will adjust the exposure levels. The adjustment can be a half stop more than 'standard grey'
(2) ISO noise speed is the S value when when the exposure generates a clear (noiseless) picture at an S/N value of 40.
(3) SOS (standard output sensitivity) is the S value when the exposure generates a picture of medium output level corresponding to 0.461 times the maximum output level (digital value around 248 in a 16-bit system).
(4) REI (recommended exposure index) is the S value when the exposure generates a picture with an adequate output level that the manufacturer recommends.
There is no information available in the Leica documentation that specifies which method or a mixture of methods that Leica uses to determine the ISO value of theM8/9. It is therefore not a surprise that the exposure metering with a handheld exposure meter differs from the exposure indication of the camera. It is my experience that the camera overexposes by a half to a full stop compared to the Gossen Digisky or Mastersix or the Sekonic L-758D (these three differ with a maximum of a half stop).