Are plants and plant canopies flat?

The shape of light sensors

Research instrumentation

Pedro J. Aphalo






Irradiance or spectral irradiance on a horizontal plane is normally used to quantify energy or photons available for photosynthesis. Here I discuss whether this is always the best approach in photobiology.


light measurement, entrance optics, diffuser geometry

Figure 1: Cosine diffuser as used to measure irradiance. Off-the-shelf D7-H type from Bentham Instruments.

1 The problem

Irradiance or spectral irradiance on a horizontal plane is normally used to quantify energy or photons available for photosynthesis. Similar measurements of irradiance in narrow bands of the spectrum or spectral irradiance measurements are used to characterize radiation features perceived by plant through photoreceptors.

Cosine response

Irradiance is defined as the flux received on a flat surface. The irradiance on the plane is proportional to the cosine of the angle of incidence of the light. To measure irradiance we use difussers with a shape similar to a flat disk. Achieving the correct response when the angle of incidence is shallow is difficult, but the conbination of a slightly raised disk and a ridge around it are effective in correcting deviations (Figure 1). The DH7 and D7 cosine diffusers from Bentham Instruments are some of the best available.

In the case of photosynthesis this makes some sense if we assume that a crop field is like a large horizontal leaf. In a closed canopy this assumtion may hold but in a canopy that does not fully cover the ground, the angle at which light is incident affects the fraction of the irradiance that is intercepted by foliage. How big this effect is depends on the structure of the canopy and with crops planted in rows, also on the orientation of the rows.

Is this all? No, light penetration, and thus the partition of the incident irradiance among leaves at different depths within a canopy depends on scattering as well as on the angle of incidence. Thus plant canopies do not behave optically as large flat light collecting surfaces.

If we consider individual plants, it is obvious that they are not flat horizontal light collectors with their multiple leaves displayed at various angles in 3D space. Leaves are the main site of photosinthesis, but considering photoreceptors, sensing is not restricted to leaves, as buds and elongating stems play a key role.

What about individual leaves? Do flat leaves behave optically as flat featureless surfaces? Probably nearly so, but not quite, especially in the case of leaves with a shinny reflective cuticle. Irradiance measured on a plane parallel to the leaf surface is relevant. Buds and stems are not flat.

2 Possible solutions

Can we do any better than just measuring irradiance or spectral irradiance on a horizontal plane? We can measure the diffuse component of daylight by occluding the solar disk, using shade bands (with position manually adjusted every couple of days) or solar tracking shade disks (motor driven). Usually used with pyranometers, but could be adapted to other sensors. Available ones are large in size, but a manually positioned shading disk contraption could be easily built and used with any existing cosine diffuser.

Alternatively, we can use sensors containing multiple detectors and a static shading structure. Available as irradiance sensors. These sensors require that all (seven) detectors are exposed to uniform irradiance, thus these sensors can be used only above a vegetation canopy.

All the approaches described above measure irradiance, using diffusers or detectors whose response to light beams at an angle are weighted by the cosine of the angle, i.e., they behave as a flat light collector.

Individual plants within a sparse canopy, capture light on leaves at multiple orientations, almost never only with horizontal leaf surfaces. Irradiance on a horizontal plane quantifies the available energy or photons per unit ground area, not the light available to isolated plants. While an ideal cosine diffuser weights incoming radiation according to the cosine of the angle of incidence, a theoretical spherical diffuser gives the same weight to radiation incoming from any angle in 3D space. A hemispherical diffuser is just half a sphere, which in terrestrial systems is usually enough and easier to design and manufacture (Figure 2).

Figure 2: Hemispherical diffuser prototype (side view). Custom-made by Bentham Instruments based on the D7 cosine diffuser. Can be used to measure hemispherical scalar irradiance or hemispherical fluence rate.
Figure 3: Hemispherical diffuser prototype (top view)

The Bentham diffusers are normally used as entrance optics of spectrometers. We will also build a shading disk so that we can measure diffuse spectral irradiance. These diffusers could be easily adapted to work as broadband sensors as we have already discussed with Bentham Instruments technical staff.

While our two types of diffusers provide differently weighted summaries of radiation, a much more complex and expensive spectrometer has been built by Gunther Seckmeyer and collaborators capable of measuring spectral radiance for more than 100 directions within 1 s. Radiance, is a 3D spatially resolved quantification of incoming radiation expressed per unit solid angle, in the case of this new instrument, describing the sky hemisphere.

3 Calibrations

We have two array spectrometers, Ocean Optics Maya 2000Pro, with the same configuration. Both were calibrated with their cosine diffusers, and one of them, in addition with a hemispherical diffuser. Calibrations were done on the same day using the same calibration lamps. Under a collimated light beam normal to the diffusers, the readings from the two spectromters and two three diffusers agree.

I have made enhancements to my R package ‘ooacquire’ that implement automatic acquisition of times series of spectra, with accurate timing, and time-based triggering. This makes it possible to acquire spectra concurrently with both spectrometers, either with similar or different diffusers.

4 Comparative Measurements

Added on 2024-07-10

When I wrote this post I did not yet have any data to show. So, now, when transferring the post from WordPress to Quarto I added this section for completeness. I also slightly edited the sections above.

The plotting and calculation of summaries in this section are done when the site content is rendered. The R code used is “folded” and can be made visible by clicking on the triangle or word “Code”.

Preliminary measurements, as could be expected, show differences in the measurements with the two types of diffusers that depend on the sun elevation and on the vegetation.

What we see below is a higher proportion of NIR light when using the dome-shaped diffuser. This is consistent with the sun occluded or not by clouds. Nearest trees were nearly 100 m away, and the diffusers approximately 1.6 m above the ground.

Two spectra measured simultaneaously with the two diffusers under clear sky conditions are shown as an example. These spectra were measured very near the time of local solar noon, on 12 June 2023 at Viikki, HElsinki, Finland.

The two spectra were measured simultaneously.

lubridate::with_tz(when_measured(diffusers.mspct), tz = "EET")
# A tibble: 2 × 2
  spct.idx when.measured      
  <fct>    <dttm>             
1 cosine   2023-06-12 13:20:00
2 dome     2023-06-12 13:20:00

The photosynthetically active radiation measured with the dome diffuser was 23% higher than that measured with the cosine diffuser.

q_irrad(diffusers.mspct, PAR(), scale.factor = 1e6)
# A tibble: 2 × 2
  spct.idx Q_PAR
  <fct>    <dbl>
1 cosine   1627.
2 dome     2003.
q_PAR <- as.numeric(round(q_irrad(diffusers.mspct[["cosine"]], PAR(), scale.factor = 1e6), -1))

viikki_bio3.geo <- data.frame(lon = 25.019212, lat = 60.226805, address = "BIO3, Viikki")

sun_elev <- round(sun_elevation(time = when_measured(diffusers.mspct[["cosine"]]),
                                geocode = viikki_bio3.geo), 0)

Almost at solar noon, under a clear sky the PAR photon irradiance was 1630 \(\mathrm{\mu mol\,m^{-2}\,s^{-1}}\) with a sun elevation of 53 degrees above the horizon.

Plotting the spectra shows that the dome shaped diffuser collects more photons than the horizontal cosine (flat) diffuser at all wavelengths.

autoplot(diffusers.mspct, range = c(290, 1100))

Plotting the two spectra after scaling them to an equal PAR photon irradiance of \(1\,600\,\mu mol\,m^{-2}\,s^{-1}\) reveals that the spectrum “seen” in each case differs.

autoplot(fscale(diffusers.mspct, range = c(400:700), f = q_irrad, target = 1600e-6), range = c(290, 1100))

At noon, the dome shaped diffuser “sees” the same red to far-red photon ratio, as in the case of these measurements the nearest trees were far away.

R_FR(diffusers.mspct) |> mutate(`R:FR[q:q]` = round(`R:FR[q:q]`, 2))
# A tibble: 2 × 2
  spct.idx `R:FR[q:q]`
  <fct>          <dbl>
1 cosine          1.09
2 dome            1.09

The dome shaped diffuser compared to the cosine diffuser “sees” a spectrum enriched by 5% in blue- compared to green light.

B_G(diffusers.mspct) |>
  mutate(`Blue:Green[q:q]` = round(`Blue:Green[q:q]`, 2))
# A tibble: 2 × 2
  spct.idx `Blue:Green[q:q]`
  <fct>                <dbl>
1 cosine                0.82
2 dome                  0.86

The dome shaped diffuser “sees” proportionally 22% more UV-A radiation than the cosine diffuser.

UVA_PAR(diffusers.mspct) |>
  mutate(`UVA:PAR[q:q]` = round(`UVA:PAR[q:q]`, 3))
# A tibble: 2 × 2
  spct.idx `UVA:PAR[q:q]`
  <fct>             <dbl>
1 cosine            0.074
2 dome              0.09 

The dome shaped diffuser “sees” relative to PAR by about 40% to 50% more UV-B radiation than the cosine diffuser.

UVB_PAR(diffusers.mspct) |>
  mutate(`UVB:PAR[q:q]` = round(`UVB:PAR[q:q]`, 4))
# A tibble: 2 × 2
  spct.idx `UVB:PAR[q:q]`
  <fct>             <dbl>
1 cosine           0.0013
2 dome             0.0019

This is just one example, at other sun elevation angles and cloud conditions the differences in the measurements using the two diffusers vary both qualitatively and quantitatively.