What is the Effective Quantum Efficiency of my Sensor?

September 23, 2014 Jack Leave a comment

Now that we know how to determine how many photons impinge on a sensor we can estimate its Effective Quantum Efficiency, that is the efficiency with which it turns such a photon flux ( $n_{ph}$ ) into photoelectrons ( $n_{e^-}$ ), which will then be converted to raw data to be stored in the capture’s raw file:

(1) $\begin{equation*} EQE = \frac{n_{e^-} \text{ produced by average pixel}}{n_{ph} \text{ incident on average pixel}} \end{equation*}$

I call it ‘Effective’, as opposed to ‘Absolute’, because it represents the probability that a photon arriving on the sensing plane from the scene will be converted to a photoelectron by a given pixel in a digital camera sensor. It therefore includes the effect of microlenses, fill factor, CFA and other filters on top of silicon in the pixel. Whether Effective or Absolute, QE is usually expressed as a percentage, as seen below in the specification sheet of the KAF-8300 by On Semiconductor, without IR/UV filters:

For instance if an average of 100 photons per pixel were incident on a uniformly lit spot on the sensor and on average each pixel produced a signal of 20 photoelectrons we would say that the Effective Quantum Efficiency of the sensor is 20%. Clearly the higher the EQE the better for Image Quality parameters such as SNR. Continue reading What is the Effective Quantum Efficiency of my Sensor? →

Banding, Perceptual, Quantization

I See Banding in the Sky. Is my Camera Faulty?

September 22, 2014 Jack Leave a comment

This is a recurring nightmare for a new photographer: they head out with their brand new state-of-the art digital camera, capture a set of images with a vast expanse of sky or smoothly changing background, come home, fire them up on their computer, play with a few sliders and … gasp! … there are visible bands (posterization, stairstepping, quantization) all over the smoothly changing gradient. ‘Is my new camera broken?!’, they wonder in horror.

Relax, chances are very (very) good that the camera is fine. I am going to show you in this post how to make sure that that is indeed the case and hone in on the real culprit(s). Continue reading I See Banding in the Sky. Is my Camera Faulty? →

Exposure, Photometry, Radiometry, Sensors

How Many Photons on a Pixel at a Given Exposure

September 22, 2014 Jack 2 Comments

How many photons impinge on a pixel illuminated by a known light source during exposure? To answer this question in a photographic context under daylight we need to know the effective area of the pixel, the Spectral Power Distribution of the illuminant and the relative Exposure.

We can typically estimate the pixel’s effective area and the Spectral Power Distribution of the illuminant – so all we need to determine is what Exposure the relative irradiance corresponds to in order to obtain the answer.

Continue reading How Many Photons on a Pixel at a Given Exposure →

Exposure, Radiometry

Photons Emitted by Light Source

September 16, 2014 Jack 6 Comments

How many photons are emitted by a light source? To answer this question we need to evaluate the following simple formula at every wavelength in the spectral range of interest and add the values up:

(1) $\begin{equation*} \frac{\text{Power of Light in }W/m^2}{\text{Energy of Average Photon in }J/photon} \end{equation*}$

The Power of Light emitted in $W/m^2$ is called Spectral Exitance, with the symbol $M_e(\lambda)$ when referred to units of energy. The energy of one photon at a given wavelength is

(2) $\begin{equation*} e_{ph}(\lambda) = \frac{hc}{\lambda}\text{ joules/photon} \end{equation*}$

with $\lambda$ the wavelength of light in meters and $h$ and $c$ Planck’s constant and the speed of light in the chosen medium respectively. Since Watts are joules per second the units of (1) are therefore $photons/m^2/s$ . Writing it more formally:

(3) $\begin{equation*} M_{ph} = \int\limits_{\lambda_1}^{\lambda_2} \frac{M_e(\lambda)\cdot \lambda \cdot d\lambda}{hc} \text{ $\frac{photons}{m^2\cdot s}$} \end{equation*}$

Continue reading Photons Emitted by Light Source →

Exposure, Perceptual, Photometry

Converting Radiometric to Photometric Units

September 16, 2014 Jack Leave a comment

When first approaching photographic science a photographer is often confused by the unfamiliar units used. In high school we were taught energy and power in radiometric units like watts ( $W$ ) – while in photography the same concepts are dealt with in photometric units like lumens ( $lm$ ).

Once one realizes that both sets of units refer to the exact same physical process – energy transfer – but they are fine tuned for two slightly different purposes it becomes a lot easier to interpret the science behind photography through the theory one already knows.

It all boils down to one simple notion: lumens are watts as perceived by the Human Visual System.

Continue reading Converting Radiometric to Photometric Units →

Exposure, Sensors

How Many Photons on a Pixel

September 10, 2014 Jack 2 Comments

How many visible photons hit a pixel on my sensor? The answer depends on Exposure, Spectral power distribution of the arriving light and effective pixel area. With a few simplifying assumptions it is not difficult to calculate that with a typical Daylight illuminant the number is roughly 11,760 photons per lx-s per $\mu m^2$ . Without the simplifying assumptions* it reduces to about 11,000. Continue reading How Many Photons on a Pixel →

Color, Photometry, Sensors

Nikon CFA Spectral Power Distribution

September 9, 2014 Jack 8 Comments

I measured the Spectral Photon Distribution of the three CFA filters of a Nikon D610 in ‘Daylight’ conditions with a cheap spectrometer. Taking a cue from this post I pointed it at light from the sun reflected off a gray card and took a raw capture of the spectrum it produced.

An ImageJ plot did the rest. I took a dozen captures at slightly different angles to catch the picture of the clearest spectrum. Shown are the three spectral curves averaged over the two best opposing captures, each proportional to the number of photons let through by the respective Color Filter. The units on the vertical axis are raw black-subtracted values from the raw file (DN), therefore the units on the vertical axis are proportional to the number of incident photons in each case. The Photopic Eye Luminous Efficiency Function (2 degree, Sharpe et al 2005) is also shown for reference, scaled to the same maximum as the green curve (although in energy units, my bad). Continue reading Nikon CFA Spectral Power Distribution →

Equivalence, Formats, Sensors

Focus Tolerance and Format Size

September 5, 2014 Jack Leave a comment

The key variable as far as the tolerances required to position the lens for accurate focus are concerned (at least in a simplified ideal situation) is an appropriate approximate distance between the desired in-focus plane and the actual in-focus plane (which we are assuming is slightly out of focus). It is a distance in the direction perpendicular to the x-y plane normally used to describe position of the image on it, hence the designation delta z, or dz in this post. The lens’ allowable focus tolerance is therefore +/- dz, which we will show in this post to vary as the square of the format’s diagonal. Continue reading Focus Tolerance and Format Size →

Perceptual, Sharpness, Spatial Resolution

MTF50 and Perceived Sharpness

September 5, 2014 Jack 7 Comments

Is MTF50 a good proxy for perceived sharpness? In this article and those that follow MTF50 indicates the spatial frequency at which the Modulation Transfer Function of an imaging system is half (50%) of what it would be if the system did not degrade detail in the image painted by incoming light.

It makes intuitive sense that the spatial frequencies that are most closely related to our perception of sharpness vary with the size and viewing distance of the displayed image.

For instance if an image captured by a Full Frame camera is viewed at ‘standard’ distance (that is a distance equal to its diagonal), it turns out that the portion of the MTF curve most representative of perceived sharpness appears to be around MTF90. On the other hand, when pixel peeping the spatial frequencies around MTF50 look to be a decent, simple to calculate indicator of it, assuming a well set up imaging system in good working conditions. Continue reading MTF50 and Perceived Sharpness →

Exposure, Information Science, IQ, Sensors

Exposure and ISO

September 5, 2014 Jack 2 Comments

The in-camera ISO dial is a ballpark milkshake of an indicator to help choose parameters that will result in a ‘good’ perceived picture. Key ingredients to obtain a ‘good’ perceived picture are 1) ‘good’ Exposure and 2) ‘good’ in-camera or in-computer processing. It’s easier to think about them as independent processes and that comes naturally to you because you shoot raw in manual mode and you like to PP, right? Continue reading Exposure and ISO →

Strolls with my Dog

Monthly Archives: September 2014