Why it works为什么行得通
Three cheap ideas三个便宜的点子
The project's design rule: chemistry does the resolution work, so the optics can stay cheap. More expansion with a modest lens beats expensive glass.
项目的设计原则：分辨率交给化学，光学就可以便宜。多胀几倍、配一个普通镜头，胜过昂贵的玻璃。
1 · Grow the sample, not the glass1 · 放大样本，而不是升级镜头
A lens cannot separate two points closer than about 0.61·λ/NA. For the 0.65 NA objective at 520 nm that is 488 nm. Expansion moves the molecules apart before the light ever reaches the lens, and the project's rule of thumb is effective resolution ≈ optical resolution ÷ E. In original-specimen units that is about 108 nm at 4.5×, and 79 nm at 10× with the 0.40 NA objective.
镜头分不开比约 0.61·λ/NA 更近的两个点。数值孔径 0.65 的物镜在 520 nm 波长下，这个距离是 488 nm。膨胀在光到达镜头之前就把分子拉开了；项目的经验公式是：有效分辨率 ≈ 光学分辨率 ÷ E。换算回原样本尺度，4.5× 时约 108 nm；换数值孔径 0.40 的物镜、放大 10× 时约 79 nm。
The lens's diffraction limit does not change; the specimen gets bigger. These are paper numbers, and still not electron microscopy: you only see what you label, and the chemistry can make its own artefacts.
Who got there first: Zhang, Chang and colleagues paired expansion with a webcam mini-microscope in 2016 ("expansion mini-microscopy"), reaching, after expansion, a resolution comparable to a benchtop microscope's on unexpanded samples, at a hundredth to a thousandth of the price. SWELL builds on their idea.
谁先做到的：Zhang、Chang 等人在 2016 年就把膨胀显微和网络摄像头做的迷你显微镜结合起来（"膨胀迷你显微"），膨胀之后，用百分之一到千分之一的价格，达到了与台式显微镜看未膨胀样品相当的分辨率。SWELL 是在他们的思路上往前走。
镜头的衍射极限一点没变，变大的是样本。这些都是纸面计算，也远不是电镜：只能看到被标记的东西，化学步骤本身还可能制造假象。
2 · A ruler grown into the meat2 · 长在肉里的尺子
E = SLpost ÷ SLpre
Sarcomere spacing is measured on the same myofibril before and after expansion. The project's notes call the period blur-invariant: blur softens each stripe but leaves the spacing alone, so the ratio survives cheap optics. The before-image should need no label: differential phase contrast with four oblique LEDs is predicted to show the stripes (the project's choice after the physics check; untested), with crossed polarisers as a cross-check.
在同一根肌原纤维上，膨胀前后各量一次肌节间距。项目笔记说这个周期“不受模糊影响”：模糊只让条纹变软，间距不变，所以便宜镜头也能用这个比值。膨胀前那张图应该不用染色：按预测，用四个斜射 LED 做差分相衬（DPC）能看到条纹（这是物理核算后项目选定的方式，未经测试），正交偏振光作为交叉核对。
It replaced the textbook A-band ruler, which needs sarcomeres long enough to show an I-band: only about 13% of supermarket breast at 4×.
它取代了教科书里的 A 带尺子。那把尺子要求肌节长到能看见 I 带，超市鸡胸肉在 4× 下只有约 13% 合格。
Who got there first: Chen, Tillberg and Boyden (2015), who introduced expansion microscopy, imaged the same cells before and after expansion and measured how far lengths moved (under 1% of the distance in cultured cells, 2–4% in brain slices). Sheard and colleagues (2019) used the periodicity of sarcomeres and the fixed width of Z-discs as intrinsic reporters of local gel expansion in heart cells, and Sheard's 2021 thesis found the sarcomere factor lower than the gel's. A 2022 thesis by Migliore expanded isolated rabbit myofibrils, imaged them without labels and used the A-band as the ruler. VISTA (Miao, Lin, Qian and Wei, 2022) measured expansion by comparing label-free images of the same structures before and after. What SWELL adds is pairing each myofibril's label-free period before expansion with its own period after.
谁先做到的：发明膨胀显微术的 Chen、Tillberg 与 Boyden（2015）就在膨胀前后拍同一批细胞，量出长度偏移了多少（培养细胞里不到距离的 1%，脑切片里 2–4%）。Sheard 等人（2019）在心肌细胞里，用肌节的周期和 Z 盘的固定宽度作为凝胶局部膨胀的内在指示；Sheard 2021 年的学位论文发现，肌节算出的倍数比凝胶的低。Migliore 2022 年的学位论文膨胀过分离的兔肌原纤维，不染色成像，并用 A 带当尺子。VISTA（Miao、Lin、Qian 与 Wei，2022）通过比较同一结构膨胀前后的免标记图像来测膨胀。SWELL 加的是：把每一根肌原纤维膨胀前的免标记周期，和它自己膨胀后的周期配对。
3 · Cheap glass, just enough of it3 · 便宜镜头，刚好够用
Motic PL 40X/0.65 and PL 20X/0.40 plan objectives, one 100 mm achromat 25 mm behind the objective, and a mono IMX296 global-shutter camera (1456 × 1088 px, 3.45 µm) at £49.87. Together: 17.8× and 0.194 µm pixels, which is 1.03× Nyquist for the 4× track and 0.84× for the 10× track.
Motic PL 40X/0.65 和 PL 20X/0.40 平场物镜，物镜后 25 mm 处放一片 100 mm 消色差透镜，再配一台 £49.87 的 IMX296 黑白全局快门相机（1456 × 1088 px, 3.45 µm）。合起来是 17.8×、每像素 0.194 µm：4× 路线达到奈奎斯特采样的 1.03×，10× 路线为 0.84×。
The stock OpenFlexure lens would undersample (0.66× Nyquist), and a colour sensor wastes signal, so neither is used. The stage would be a fork of the open OpenFlexure Microscope v7, run by a Raspberry Pi 5 and a Pico 2.
OpenFlexure 自带的镜头会欠采样（只有奈奎斯特的 0.66×），彩色传感器又浪费信号，所以都不用。载物台将改自开源的 OpenFlexure 显微镜 v7，由树莓派 5 和 Pico 2 控制。
Built on open work: the OpenFlexure Microscope (Collins et al., 2020; build docs), expansion microscopy (Chen, Tillberg & Boyden, 2015), expansion mini-microscopy (Zhang, Chang et al., 2016), sarcomeres as intrinsic expansion reporters (Sheard et al., 2019), U-ExM (Gambarotto et al., 2019), pan-ExM (M'Saad & Bewersdorf, 2020) and TREx (Damstra et al., 2022). Every source, with what SWELL took from it, is listed under credits.
站在这些公开成果的肩膀上：OpenFlexure 显微镜（Collins 等，2020；搭建文档）、膨胀显微术（Chen、Tillberg 与 Boyden，2015）、膨胀迷你显微（Zhang、Chang 等，2016）、以肌节作为膨胀的内在指示（Sheard 等，2019）、U-ExM（Gambarotto 等，2019）、pan-ExM（M'Saad 与 Bewersdorf，2020）和 TREx（Damstra 等，2022）。所有出处，以及 SWELL 从中借了什么，都列在致谢里。
Words on this page本页用到的词
A short glossary简明词汇表
- Sarcomere
- One repeating unit of a muscle fibre, about 1.69 µm long in supermarket chicken breast. A muscle contracts by shortening them.
- Myofibril
- A thin thread inside a muscle cell, made of sarcomeres joined end to end. SWELL uses them as rulers.
- Z-disc
- The thin line where one sarcomere meets the next.
- Expansion factor (E)
- How many times bigger the gel made the sample: a length after expansion divided by the same length before.
- Eax and Etr
- The expansion factor along a myofibril (axial) and across it (transverse).
- Anisotropy
- Growing more in one direction than another. On this page it is Eax ÷ Etr − 1.
- Non-affine
- A distortion that no single stretch, shift and turn of the whole gel can explain, such as a tear or a fold.
- PSF
- Point spread function: the blurred spot a microscope makes of a single point of light. The narrower it is, the finer the detail you can see.
- Nyquist sampling
- Taking at least two pixels across the finest detail you want to see. With fewer, that detail is lost.
- Strehl ratio
- How bright the peak of a focused spot is compared with a perfect lens's, from 0 to 1; 1 means no aberration. On this page it is computed in simulation, relative to the gel's surface.
- q
- The number the label-free stripe test hangs on: stripe contrast × √(photons per sample). The higher q is, the more precisely the stripe spacing can be read.
- DPC
- Differential phase contrast: lighting a clear specimen from one side, then the other, and comparing the two images, so thin transparent structures show up without a stain.
- Clock tile
- One patch of the gel imaged again every 50 tiles during a scan, so that slow swelling during the scan can be measured and taken out.
- Overview camera
- A small camera that photographs the whole gel, to measure its overall size before and after expansion.
- CMR
- Carcinogenic, mutagenic or toxic for reproduction: hazard classes some gel chemicals carry. UK law restricts selling them to the public.
- G0
- The first gate in SWELL's plan: a complete, checked design on paper, before any part is bought or any gel is made. SWELL hasn't passed it.
- Simulated, synthetic
- Made by a computer from a model, not measured on anything real.
- 肌节
- 肌纤维里一节一节重复的单位，超市鸡胸肉里长约 1.69 µm。肌肉收缩，就是肌节在变短。
- 肌原纤维
- 肌肉细胞里的细丝，由肌节一节接一节串成。SWELL 把它们当尺子用。
- Z 盘
- 一个肌节和下一个肌节交界处的那条细线。
- 膨胀倍数（E）
- 凝胶把样品放大了多少倍：膨胀后的某段长度除以膨胀前的同一段长度。
- Eax 和 Etr
- 沿着肌原纤维方向（轴向）和横着它的方向（横向）的膨胀倍数。
- 各向异性
- 往一个方向胀得比另一个方向多。本页里它是 Eax ÷ Etr − 1。
- 非仿射
- 整块凝胶任何一次统一的拉伸、平移和旋转都解释不了的形变，比如裂开或折叠。
- 点扩散函数（PSF）
- 显微镜把一个光点拍成的那个模糊小斑。它越窄，能看清的细节越细。
- 奈奎斯特采样
- 要看清的最细的细节上，至少要占两个像素。少了，这个细节就丢了。
- 斯特列尔比
- 聚焦光斑的峰值亮度和完美镜头相比是多少，在 0 到 1 之间；1 表示没有像差。本页里它是在模拟中、相对凝胶表面算出来的。
- q
- 免标记条纹检验所依赖的那个数：条纹反差 × √（每个采样点的光子数）。q 越大，条纹间距读得越准。
- 差分相衬（DPC）
- 先从一侧、再从另一侧照亮透明的样品，比较两张图，让薄而透明的结构不染色也能显出来。
- 时钟视野
- 扫描时每拍 50 个视野就回去重拍一次的同一块凝胶，用来测出并扣掉扫描过程中缓慢的膨胀。
- 全景相机
- 拍下整块凝胶的小相机，用来量凝胶膨胀前后的整体大小。
- CMR
- 致癌、致突变或有生殖毒性：一些凝胶化学品带有的危害类别。英国法律限制把它们卖给公众。
- G0
- SWELL 计划里的第一道关卡：在买任何零件、做任何凝胶之前，有一份完整、经过检查的纸面设计。SWELL 还没有通过它。
- 模拟、合成
- 电脑按模型算出来的，不是在真实的东西上测出来的。