Selection of appropriate LEDs for the lighting field
The spectral irradiance throughout this study was measured with an array radiometer (Newport OSM400, Newport Spectra-Physics GmbH, Darmstadt, Germany with a UV/VIS range from 200-800 nm, spectral resolution of 1 nm, a Sony CCD-Sensor with 2046 pixel, and a slit with of 50 µm). From individual LED spectra by superimposing the individual LED spectra LEDi(λ) a desired target spectrum can be simulated as a linear combination of individual spectra multiplied with a proportion coefficient xi (equation (2)). The number of xi and LEDi(λ) is depending on how many individual LED spectra are present; in this work the number is restricted to 23, i = 1, . . . , 23. The desired target spectrum can be arbitrary depending on the experimental application, for example the solar spectrum at a certain time or solar zenith angle or at the floor of a dense forest canopy. The simulated spectrum Ssimulated results by the following equation (2):
How the proportion coefficients xi were determined will be explained in the subsection ‘Non-negative least squares for solving multi coefficient linear regression’ (see below). As prerequisite for the calculations, a market research was conducted to determine which LEDs with a certain wavelength and sufficient radiant power are commercially available. The list of the selected ‘high power’ LEDs is given in the Supplementary Information (Table S1). The Sunlike LEDTM from Seoul Semiconductor (Seoul Semiconductor Europe GmbH, Munich, Germany) is a so-called ‘white’ LED with a wide emission spectrum, which provides the basic irradiance for the new lighting system.
‘White’ LEDs produce their emission spectrum in the following way: A blue LED with an emission of c. 450 nm excites a mixture of fluorescent substances by its short-wave emitted spectrum. Depending on the composition of the fluorochromes, this mixture emits lower-energy wavelengths in various spectral ranges and thus generates ‘white’ light . The special feature of the Sunlike LEDTM is that - compared to conventional ‘white’ LEDs - the excitation of the light source is done by means of an ultraviolet LED with a wavelength of c. 405-420 nm and a special combination of fluorescent materials. This results in a ‘white’ spectrum that radiates a sufficiently high power in this spectral range already from a wavelength of 420 nm.
The phosphor composition of the Sunlike LED ensures a relatively uniform radiation in the range of 420-700 nm. By using such a ‘white’ LED as backbone of the lighting system, the total number of required LEDs could be significantly reduced. Manufacturers of ‘white’ LEDs express the radiated power in lumen in their data sheets, and in most cases the standardized spectral distribution is also given in the form of a graph. For the present work, overall, the curves of 23 LED emissions, as specified by the manufacturers, were digitized by software (Engauge Digitizer Version 10.11) or approximated by a Gaussian distribution. These spectra were then used further for our calculations.
For the first basic calculations, which were necessary for the selection of the different LEDs, it was sufficient to represent the emission spectra of the different LEDs by digitized spectral distribution or by Gaussian distribution. In most data sheets of the LED manufacturers the following parameters are given: The typical dominant wavelength, the spectral bandwidth (FWHM) and the radiant flux (R) All these specifications are only typical values and vary depending on the binning (grouping of LED parameters) of the LEDs. For a homogenous distribution of radiation, only LEDs with a beam angle of more than 110° were used.
For many LEDs emitting in the visible range (400-700 nm), the radiant power is specified in the data sheet in the unit lumen. For further calculations it was therefore necessary to convert from lumen to W.
With the help of the parameterization of all LED specifics, it was now possible to calculate the required number of individual LEDs using an algorithm to synthesize the desired target spectrum (e.g. Fig. 3). To find the optimal parameters xi a special algorithm was applied (see next section).
Later on, this algorithm was applied to synthesize a target spectrum by using the measured individual LED spectra (Fig. 1c)
Non-negative least squares for solving multi coefficient linear regression
In the present work, the algorithm was programmed with R v3.5.1 (R Core Team, 2018), which includes the package ‘nnls’. This nnls-package (non-negative least squares) is an implementation of Lawson-Hanson NNLS (Lawson and Hanson, 1995) to solve the problem min || Ax – b ||2 with the constraint x ≥ 0 where x ∈ Rn , b ∈Rm and A is a m by n matrix.
In this work, the vector bi , i = 1, . . . , m, represent the target spectrum Starget(λ) [Wm-2nm-1] , b1 is the target spectrum Starget(280 nm) and b2 Starget(281 nm) until b1,020 Starget(1300 nm) in 1 nm units. L11 to Lm1 is the spectral distribution of LED1(λ) [Wm-2nm-1], in the range of 280 nm - 1300 nm in 1 nm units, L11 to L1n are the n-LED(λ) [Wm-2nm-1], in this work the number of n, the number of individual LED types, is restricted to 23. This results in a linear regression model (equation (3)) with r a n-vector of residual and x a n-vector of calculated coefficients.
The calculations revealed that a very high density of LEDs and / or a high power of LEDs is required to achieve an integrated irradiance (360-800 nm) of about 580 Wm-2 at a distance of 1.6 meter. The LED irradiance describes the part of the energy that is radiated in form of electromagnetic waves. The biggest part of the rest energy (depending on the efficiency of the individual LED types) will be released by thermal conduction and thermal convection. This means that for an LED-based lighting system, with such a high irradiance, the LEDs must be equipped with a very efficient cooling system. The main cooling part of our system became realized by an in-house developed and constructed 18 kg active, water-cooled heat sink (see Supplementary Fig. S4g). The heat sink is made of aluminum due to its good thermal conductivity of 220 W K-1 m-2 (76Kuchling 2014 in die ref). With a size of 53 cm x 53 cm the heat sink offers space for 81 circuit boards and their cabling (see Supplementary Fig. S4a).
LED-drivers and control unit
A small change in voltage at the LED leads to a large change in current. For this reason, electronic ballasts designed as constant current sources were used for this work. For the operation of the LED circuit boards, described above, a constant current ballast is required. Depending on the composition of the LED circuit board and the number and type of LEDs, a ballast must be selected that supplies the required forward voltage of the LEDs connected in series as well as the required current. Six different ballasts were used (see Supplementary Table S1).
The ballasts have an open-circuit, short-circuit and overtemperature shutdown as protective functions. According to the manufacturers’ protocol, they have a life of more than 50,000 h at a housing temperature below 75°C. A very important aspect that these ballasts fulfil is the control of the LED radiation intensity, not by pulse width modulation (PWM), but by controlling the current intensity. Regardless of whether the dimming signal is sent to the ballasts via the DALI interface or via 0-10V, the dimming behavior or the change in current intensity is linear to the dimming signal. However, each output of the constant current ballast (LED driver) has a specific AC component, this is called ‘ripple’ and is specified for these ballasts at less than 5%. Own measurements with an oscilloscope have shown that the residual ripple at 60% load is < 2%. The frequency of the alternating current component is in the range above 2 kHz. Such ripples can be considered as small compared to traditional light sources operated by alternating voltage . The supply voltage of the ballasts is realized via the 230 V AC mains
The lighting control system DALI (Digital Addressable Lighting Interface, industry-standardized protocol, specified in IEC 62386) is a serial bus system based on two lines for controlling lamps. The DALI system is part of IEC 62386, which defines a standard protocol for communication between lamps, sensors and ballasts. The controller / master sends a 16 bit Manchester code, the ballasts respond with an 8 bit Manchester code. A controller / master can control up to 64 ballasts on the two-line serial bus. It is also possible to use several masters and increase the number of digitally addressable ballasts. In this thesis a controller was used which contain four masters and thus control 256 ballasts individually. One DALI line allows the management of 16 different groups and 16 different scenes. A scene contains up to 64 different ballasts and a specific dimming level for each ballast 
Assembly of circuid boards
In order to operate the large number of LEDs required for this lighting system, we arranged them in a series connection. When the LEDs are connected in series, the individual forward voltages add up to a total voltage which is applied to the series connection. However, the current is the same for each LED and thus typically also the radiated power. Since practically all ‘monochromatic’ high-power LEDs are SMD (Surface Mounted Device), it was necessary to develop a printed circuit board (PCB) on which the LEDs can be soldered and connected in series (see Supplementary Fig. S4 d, e, f). Three different PCBs or layouts were developed for this purpose using the AUTODESK-EAGLE version 9.4.1 software (AUTODESK, San Rafael, USA). Common to all layouts is that the LEDs are symmetrically arranged in a small space and connected in series. In order to keep the ohmic losses on the boards as low as possible, the copper track thickness was chosen to be 105 µm and the width of the individual connections of the LEDs from the cathode to the anode, the next LED, was increased to the width of the LEDs. The base material of the circuit boards is 1.6 mm thick aluminium. A thin layer / foil of dielectric was applied to this aluminium. Then the copper conductor paths, the copper thermal pads for the LEDs and the pads for the anode and cathode were applied. A white solder resist prevented the solder from running during the soldering process and still acts as a reflective surface when used as a light-engine.
After the production of the circuit boards the soldering paste was applied exactly to the solder pads of anodes and cathodes with a stencil. The LEDs were mounted and soldered in a plasma SMD soldering process, the production of the PCBs and the mounting and soldering of the LEDs was done by an outside company.
The number of LEDs connected in series depends on the LED drivers used. These have a defined voltage range in which they can supply the LEDs with constant current. For the developed LED light system 5 different designs for the circuit boards were developed (see Supplementary Fig.4 b, c, d, e, f). For the high power SMD LEDs with a footprint of 3.3 x 3.3 mm, 56 LEDs were connected in series on a PCB (see Supplementary Fig. S4d). For LEDs with a footprint of 2.7 x 2.7 mm a special layout with 56 LEDs connected in series on a PCB (see Supplementary Fig. S4e). In case of SMD LEDs with a footprint of 5x6 mm, 36 LEDs were connected in series also on a special PCB layout (see Supplementary Fig. S4f).