## 1 Introduction  
_Haematococcus pluvialis_ is a unicellular green microalgae known for its accumulation of astaxanthin to 5% of its dry weight [1, 2]. Due to its powerful antioxidant activity, natural astaxanthin from algae is being produced and increasingly applied in the medical and nutraceuticalal industries [2]. Currently, _H. pluvialis_ can be cultivated in two ways to obtain biomass, as well as astaxanthin. The traditional method is cultivation in a suspension, often separated into two phases: a first phase comprising the production of green cell biomass and a second, astaxanthin accumulation phase involving red akinetes [3, 4]. A disadvantage of the suspension culture is its relatively slow growth and low final cell densities, resulting in high energy requirements for harvesting the biomass [5, 6].  
The second method for cultivating _H. pluvialis_ is immobilized culturing, in which microalgae are fixed to form a biofilm on a layer that serves as a substrate [7, 8, 9, 10, 11]. Various types of biofilm-based photobioreactors have been developed, including submerged systems and porous substrate photobioreactors (PSBRs) [12]. In submerged systems, the algal biofilms are submerged in the medium from which they take up nutrients [8, 12]. In PSBRs,the biofilm is separated from the medium by a microporous substrate, and the surface of the biofilm is in contact with the ambient atmosphere [12; 13]. In their most popular configuration, the twin-layer PSBR (TL-PSBR), PSBRs have been experimentally tested on a wide variety of algae [12; 13; 14; 15; 16], and the dynamics of their biofilms have been characterized and modelled in some detail [17; 18; 19; 20; 16]. When applied to _H. pluvialis_, immobilized cultivation is usually a one-phase culture, as the algae increase in biomass and turn red to produce astaxanthin simultaneously with biofilm [15; 21].  
In Vietnam, angled biofilm-based PSBRs for _H. pluvialis_ have been successfully designed and operated [21; 22]. This system shows potential for the production of astaxanthin from _H. pluvialis_ at the bench- and pilot-scales. To prepare initial green algal biomass, _H. pluvialis_ is usually cultured in a suspension with increasing volumes. Algae are then collected after about 20-25 days of cultivation by centrifugation. After centrifugation, the concentrated algal suspension is applied to the substrate layer to grow into the biofilm [2; 15; 22]. With a usual initial biomass density of 5-7.5 g\(\cdot\)m\({}^{-2}\), the volume of algal culture needed to inoculate 1 m\({}^{2}\) biofilm is about 15-20 L [15; 21; 22]. Therefore, the process of growing algae in a suspension to inoculate biofilms in PSBRs is still an issue that needs to be solved when upscaling astaxanthin production to the pilot scale [21].  
In _H. pluvialis_ cultivation, high light intensities, up to 2000 umol photons m\({}^{-2}\cdot\)s\({}^{-1}\) sunlight, have been shown to be the most important single factor for the induction of astaxanthin accumulation [4; 23]. In contrast, low light intensities, below 100 umol photons m\({}^{-2}\cdot\)s\({}^{-1}\), are often used to maintain and increase the density of microalgae in a suspension in the green phase [24; 25; 26; 27]. However, the effects of low-light intensity on the growth and cell divisions of _H. pluvialis_ in TL-PSBR biofilms have previously not been studied in detail [15]. Following the above analysis, a small-scale angled PSBR was used to grow green-stage _H. pluvialis_ to take advantage of immobilized cultivation to address the problem of inoculation of the PSBR. In this study, we focused on the determination of the light intensity most suitable for the growth and maintenance of the vegetative green stage of the algal cells. Moreover, the initial biomass (inoculum) density of the biofilm was also optimized to achieve the highest dry biomass yield.