tisdag 18 oktober 2011

IR Detectors and True-SB

In the previous post From Correct Planck Law to True-SB and False-SB I derived the following Stefan-Boltzmann Law based on the new proof of Planck's radiation law presented in Computational Blackbody Radiation in Slaying the Skydragon:

(True-SB) $R(T,T_b) =\int_{T_b}^{T}\gamma T f^2 df + \int_0^{T_b}\gamma (T - T_b) f^2df \equiv I_1 + I_2$,

where $R(T,T_b)$ is the radiance from a blackbody of temperature $T$ into a blackbody background of temperature $T_b < T$.

Here the first integral $I_1$ is the radiance from the blackbody absorbed as heat by the background above the cut-off of the background and $I_2$ the net heat absorbed below cut-off as the difference between absorbed and emitted radiation.

Let us see what (True-SB) can tell us about the possible design of IR detectors, where $T$ is the temperature of the object to be detected and $T_b$ that of the detector. There are two types of detectors to consider (see here):
  1. cooled with $T_b < T$
  2. un-cooled with possibly $T_b > T$.
In a cooled detector with $T_b < T$ both $I_1$ and $I_2$ are positive and $R(T,T_b)$ can
be directly recorded as heating transferred into an electric signal by a thermocouple. (For a star a large distance only $I_1$ is recorded, with the help of optical magnification of the input,
but this is not IR.)

In an un-cooled detector the heat transfer would be away from the detector if $T_b>T$, and
in principle the object could be detected from recording the cooling of the detector. But this is
a form of negative detection which may be difficult to get to work in practice.

More interesting is to explore what (True-SB) suggests for the design by heating in the case the object has lower temperature than the detector:

In this case the signal from the object does not contain frequencies above the cut-off of the detector and so $I_1=0$, but by magnifying the signal optically (by a lense) the radiation below cut-off can be changed into
  • $I_2(M)= \int_0^{T_b}\gamma (MT - T_b) f^2df$
where $M>1$ is a magnification factor and $I_2(M)$ may thus become positive even if $T_b > T$.

We sum up the experience from (True-SB):
  1. If the temperature of the detector is lower than the object, then direct recording of heating is possible (with $I_1>0$ and possibly also $I_2>0$ ).
  2. If the temperature of the detector is higher than that of the object, then heating may be recorded after optical input magnification (with $I_2>0$).
Note added: I made a mistake believing that a lens can magnify radiance, which I correct in Learning by Seeing.

9 kommentarer:

  1. In the real world, photon detecting systems have no trouble detecting objects cooler than themselves. Never have, never will. You already showed the WMAP image of the cosmic microwave background, so here are two easy questions: 1. what is the approximate temperature of the CMB? 2. what is the approximate temperature of WMAP's detectors?

  2. By optical magnification the intensity of the light from the cold object is increased and can thus cause heating of the detector and detection. The same as in the case of a microwave oven.

  3. What is being magnified? No energy can travel from a cold body to a hot body.

  4. There is nothing to magnify. As you have demonstrated, we cannot receive radiation from a colder body. It doesn't exist. So, what is being detected?

  5. Very good question: It appears that a lens concentrates light and thus must
    consume some energy in order not to violate the 2nd law. I will return this

  6. You are right: the detector cannot reach higher temp than the target even with a lens, see the new post http://claesjohnson.blogspot.com/2011/10/learning-by-seeing.html

  7. And so what is being detected by the WMAP satellite, that is (obviously wrongly) being interpreted as cosmic microwave background? Because if the atmosphere can't emit detectable radiation towards Earth, then obviously the CMB can't.

  8. Good question: But it is possible to detect electromagnetic waves
    without relying on their thermic heating potential, by using instead resonance just like a radio antenna which upon excitation by incoming electromagnetic waves can deliver a signal which can be amplified to detection. Resonance does not connect to internal heating and thus does not have the frequency-temperature restriction imposed by the 2nd law.
    I will expand in a new post.

  9. No, it can't be possible to detect them from the CMB, or the atmosphere, because according to your theory there is no emission at all from a colder body to a hotter one. So, what is this supposed CMB?

    Unless energy is being transferred, detection is impossible.