Curt MobleySequoia Scientific, Inc.

2700 Richards Road, Suite 107425-641-0944 ext 109

curtis.mobley@sequoiasci.com

www.curtismobley.com

Heavy stuff!!

relevant to this lecture:"The beginning of wisdom is calling things by their correct names." Antisthenes, 5th century B.C., Greece

relevant to the entire course:“Is it not pleasant to learn and to review constantly what one has learned?”Confucious, 6th century B.C., China

relevant to my lectures:“Do not worry about your difficulties in mathematics; I can assure you that mine are still greater." Einstein, 20th century A.D., USA

Where we’re going today:

Overview of quantities needed for this course: How do you quantitatively describe how much light there is, where it is going, etc.?

(ref: Light and Water, Chapter 1)

What is light?

How to specify directions

Radiance--the fundamental quantity for describing light

Irradiances--often more useful

Remote-sensing reflectance--fundamental to ocean color remote sensing

Pretty picture

Light and Water, p 143

Light consists of elementary particles called photons,which are characterized by their• wavelength (or frequency )• state of polarization

Photons• carry energy and (linear and angular) momentum• have no detectable physical size (point particles, like electrons??)• always travel at the same speed in vacuo

Both wave and particle properties are always present, and this wave-particle duality cannot be described by classical physics; you must always use quantum mechanics and special relativity theory when describing photons.

However, you can use either the wave or the particle properties to describe light, depending on which is convenient for your particular problem (e.g., photons are created or destroyed like particles, but propagate like waves). You will measure either the wave or particle properties of light, depending on the measurement device being used in the experiment.

No one knows what photons actually are, but their behavior can be predicted.

Warning on directions:

In radiative transfer theory (i.e., inthe radiative transfer equation, in Light and Water, and in HydroLight), and always refer to the direction the light is going.

Experimentalists often let and refer to the direction the instrument was pointed to measure the radiance.

I call the instrument direction the viewing direction, v and v, where v = - and v = + .

Radiance is always a bit hard to plot because of so many variables.

Example plot: L(z, , , ) as a function of z and for the nadir-viewing direction (aka the upwelling radiance Lu: light traveling straight up, detector pointed straight down)

1E-121E-111E-101E-091E-081E-071E-061E-05

0.00010.001

0.010.1

1

350 400 450 500 550 600 650 700 750

wavelength [nm]

Lu

[W

/(m

^2

sr n

m)]

0

10

20

30

40

50

Another example plot: L(z, , , ) as a function of and at z = 5 m depth and in the plane of the sun.

Note: +z is downward, so = 0 is light heading straight down, viewed by looking straight up in the v = 180 deg direction.

Example plot: Ed as a function of depth and wavelength

1E-101E-091E-081E-071E-061E-05

0.00010.001

0.010.1

110

350 400 450 500 550 600 650 700 750

wavelength [nm]

Ed

[W

/(m

^2

nm

)]

0

10

20

30

40

50

Another example plot: Ed as a function of depth for 3 selected wavelengths

1.00E-061.00E-051.00E-041.00E-031.00E-021.00E-011.00E+001.00E+01

0 10 20 30 40 50

depth [m]

Ed

[W

/(m

^2

nm

)]

405 nm

505 nm

605 nm

Ed(λ)

Lr(θ,φ,λ)

Lt(θ,φ,λ)

Lw(θ,φ,λ)

Lu(θ,φ,λ)

Lu(θ,φ,λ) = Lw(θ,φ,λ) + Lr(θ,φ,λ)

Rrs(θ,φ,λ) =

upwelling water-leaving radiancedownwelling plane irradiance

= Lw(θ,φ,λ)/Ed(λ) [sr-1]

Remote-sensing Reflectance, Rrs

The foundation for ocean color remote sensing

Warning on spectral vs band-integrated radiance and irradiance:

For example, spectral downwelling plane irradiance Ed() is per unit wavelength interval, with units of W m-2 nm-1.

Band-integrated downwelling plane irradiance is the spectral irradiance integrated over some finite wavelength band, e.g.,Ed420410Ed()d[Wm2]Ed420410Ed()d[Wm2]Note: PAR is always a band-integrated quantity.

Another warning:

When reviewing papers I sometimes get “…and the measured irradiance was .75.”

Which irradiance? Ed, Eu, Eo…?

What units? W m-2 nm-1, W cm-2 m-1, W m-2…?

Is the magnitude 0.75, or is the . a fly spec, in which case the magnitude is 75?

Sloppy notation and terminology+ no units or inconsistent units = PAPER REJECTED!!(ditto for figures without axes labeled)

“…and the measured downwelling spectral plane irradiance was 0.75 W m-2 nm-1. For brevity we henceforth call this the irradiance E.”

Rainbows (I can’t remember where, but somewhere out West,many years ago). There is much to see here: the order of the colors is different in the two bows, the sky appears darker between the bows, there is scattered white light on the inside of the primary bow, but not on its outside, etc. A polarizer will reveal much more….