Notes by Dr. Optoglass: Sensitivity and ISO of the Human Eye

Topics Covered:

  • Sensitivity
  • ISO
  • The ISO Range of the Human Eye
  • Photography to the amateur is recreation, to the professional it is work, and hard work too, no matter how pleasurable it my be – Edward Weston

    A camera sensor (or film) is like a sponge:

    It has the ability to soak in light. How does this ability affect the exposure?

    Here’s the formula for exposure once again:
    EV vs ISO
    where
    EV is the exposure value
    N is the f-number
    t is the shutter speed in seconds
    S is the ISO arithmetic speed
    E is the illuminance in lux
    C is the incident-light meter calibration constant

    For a given exposure, the third formula clearly shows S is inversely proportional to the illuminance.
    Lux vs ISO

    In other words, when the light level reduces, the sensor must soak up more of whatever light is available to give the same exposure. When the light rises, the sensor must soak up less light to give the same exposure. Is the ability of the sensor to act like a sponge unlimited?

    Definitely not. Every sensor or film has a limited sensitivity. It has a minimum range and a maximum range. This range is called the sensitivity of the sensor.

    ISO

    Since aperture and shutter speed are changed in ‘stops’ (fixed values) – with each stop doubling or halving the light – the sensitivity of the sensor or film is also measured in stops. The standard that is currently in vogue is the ISO standard (short for International Organization for Standardization).

    The ISO standard is defined in two ways – linear and log (Since the formula for exposure is related to aperture and the shutter by a log function). Most of the time, though, the log value is ignored, and the ISO value displayed or talked about is the arithmetic value. The ISO arithmetic scale directly corresponds to the ASA standard of rating film. The ISO log scale directly corresponds to the DIN standard of rating film. The ISO range is also called the Exposure Index (EI).

    The formula to convert the arithmetic ISO value to the logarithmic ISO value is

    where
    S is the arithmetic ISO (the same used in the formula for EV)
    So is the log ISO value

    The arithmetic value in absolute stops are 0.8, 1.6, 3, 6, 12, 25, 50, 100, 200, 400, 800, 1600, 3200, 6400, and so on.

    Modern camera manufacturers rate their cameras beyond 10,000 ISO as follows: 12800, 25600, 51200, 102400, 204800. Values in between that represent half a stop, a third of a stop, etc are also available on some cameras.

    The f-number is based on a well-defined strict standard (mm), and the shutter speed is based on a well-defined strict standard (s), but the ISO – even though specified in detail – is still at the mercy of how camera manufacturers choose to measure their devices. No two sensors are alike.

    ISO Range of the Human Eye

    A camera sensor has a limited and fixed ISO range – the human eye does not behave similarly. When in low light, the rods are excited, and as we have seen, a single photon can excite a single rod in the human eye. However, the eye needs some time to adjust to low light, and don’t have the luxury of long exposures like a still camera.

    Point being, there is no direct comparison. It’s like asking what the gas mileage of a human being is. Still, for fun’s sake, we can make some calculations. Here’s a formula:

    where
    H is in lux seconds
    L is the luminance of the scene (in nits)
    t is the exposure time (in seconds)
    N is the aperture f-number
    q is π/4, a factor taking into account transmission, vignetting and the angle relative to the axis.

    This formula is used for digital cameras. What if we could measure the eye like a digital camera, and just showed the results to people?

    Assuming the lowest lux level is 0.0001 lux, at an f-number of f/2, with an exposure time of 30 minutes (the time it takes the rods to become most sensitive in low light), the value of H-low is 0.11.

    To the higher extreme, the maximum lux level that the eye can withstand might be about 35,000 (direct sunlight at noon is about 130,000 lux – but we can’t look at the sun, can we?) lux. At this level, our eye stops down to f/8 and for fun’s sake let’s assume the shutter is 1/48s. H-high is then about 55.

    The formula for ISO saturated is:

    where
    Ssat is the ISO based on saturation
    Hsat is the values we got above for H in lux seconds

    For these values, the lower ISO is about 1.4 and the higher ISO is about 709. I’d say from this we can assume the ISO range of the eye is from 1 to 800 ISO.

    Takeaways:

  • In addition to aperture and shutter speed, the exposure of a system also depends on the sensitivity of its sensor.
  • ISO is a standard that defines sensitivity in stops of light.
  • The ISO range of the human eye is from 1 to 800 ISO.
  •  
    Links for further study:
    http://en.wikipedia.org/wiki/Film_speed
    http://en.wikipedia.org/wiki/Image_sensor
    http://en.wikipedia.org/wiki/Adaptation_(eye)

    Next: Dynamic Range of the Human Eye
    Previous: The F-numbers of the Human Eye


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    August 10, 2012

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