🌊 微光花園 World 2：對比海灣Micro Bloom · World 2: Contrast Cove
⭐ 0🌸 0
▼ 點一下或按 A 繼續Tap or press A
Micro BloomWorld 2 · 對比海灣World 2 · Contrast Cove
⏸ 暫停Paused
⚙️ 設定Settings
語言Language
🎵 背景音樂Music
🎼 曲目Track
🕹️ 螢幕搖桿On-screen controller
💬 劇情提示Story & hints
🔔 音效Sound effects
⛶ 全螢幕Full screen
🖥️ 繪圖Renderer
✨ 畫質Quality
1280×720 · 1920×1080 · 2560×1440 (2K)
設定會記在這台裝置的瀏覽器中。若裝置不支援 WebGPU，會自動改用軟體繪圖。Settings are remembered in this browser. If WebGPU is not available, the game switches to software rendering automatically.
💾 存檔／讀檔Save / Load
自動Auto
槽位 1Slot 1
槽位 2Slot 2
槽位 3Slot 3
存檔保存在這台裝置的瀏覽器中，過關時會自動存檔。快速鍵： 存到槽位 1、 讀取槽位 1。在關卡中存檔，讀檔後會從該關開頭重新開始。清除瀏覽器資料會刪除存檔，請用「匯出」備份。Saves stay in this browser on this device; the game also autosaves after every stage. Hotkeys: saves to slot 1, loads slot 1. A save made inside a stage restarts that stage from its beginning. Clearing browser data erases saves, so export a backup.
⌨️ 自訂按鍵Custom keys
上Up
下Down
左Left
右Right
A（確定）A (confirm)
B（返回）B (back)
暫停Pause
提示Hint
快速存檔Quick save
快速讀檔Quick load
按「變更」後再按下想用的鍵（Esc 取消）。Enter 永遠可當 A，Esc 永遠可當返回／暫停。也支援 USB／藍牙手把。Press Change, then the key you want (Esc cancels). Enter always works as A, and Esc always works as Back / Pause. USB / Bluetooth gamepads also work.
⭐ Star Quiz
🌟 過關！Stage clear!
★★★
📖 精靈圖鑑與概念明信片Sprite album & concept postcards
📘 遊戲說明書How to play
🌊 故事Story
World 1 打倒糊糊菇後，微光花園重新綻放。X 光精靈「叮叮」帶著皮普和夥伴們來到「對比海灣」。這裡的亮處和暗處被搗蛋鬼「影子菇」搞混了：亮的不一定重，暗的不一定輕！After Blurshroom was defeated in World 1, the Micro Garden bloomed again. Zing the X-ray leads Pip and friends to Contrast Cove, where the prankster Shadowshroom has mixed up light and shadow: bright is not always heavy, and dark is not always light!
要點亮「X 光水晶燈塔」，你得學會讀懂影像對比、把影像變成數字，最後認識特性 X 光。已經改邪歸正的糊糊菇也會一起幫忙。To light the X-ray Crystal Lighthouse you will learn to read image contrast, turn images into numbers and meet characteristic X-rays. Blurshroom, now a friend, helps too.
同一個部落格上若有 World 1 的存檔，開始新遊戲時會自動帶入 World 1 的夥伴與花瓣。If this blog has a World 1 save in your browser, a new World 2 game brings your World 1 friends and petals along.
🎮 操作Controls
- 鍵盤：方向鍵移動／調整滑桿，空白鍵或 Enter 確定，Backspace 返回，P 暫停，H 提示（可在「自訂按鍵」更改）。Keyboard: arrow keys move / adjust sliders, Space or Enter confirm, Backspace back, P pause, H hint (change them in Custom keys).
- 滑鼠／觸控：在花園點地面，皮普就會走過去；點平台可進入關卡；滑桿可直接拖曳。Mouse / touch: tap the ground and Pip walks there; tap a pad to enter a stage; drag sliders directly.
- 螢幕搖桿：在設定或下方按鈕開啟，左邊十字鍵、右邊 A（確定）與 B（返回）。On-screen controller: turn it on in Settings; D-pad on the left, A (confirm) and B (back) on the right.
- 也支援 USB／藍牙手把。USB / Bluetooth gamepads also work.
- 💡 提示按鈕：重播本關的講解。📖 圖鑑：看精靈與明信片。💡 Hint replays the stage explanation. 📖 Album shows your sprites and postcards.
🌼 如何種花How to plant flowers
- 收集花瓣 🌸：新遊戲送 20 片花瓣，另外加上 World 1 剩下的花瓣。第一次過關，每顆星換 12 片；重玩過關每顆星換 4 片。左上角的 🌸 是目前的花瓣數。Collect petals 🌸: a new game starts with 20, plus any petals left over from World 1. A first clear gives 12 petals per star; a replay gives 4 per star. The 🌸 counter at the top left shows how many you have.
- 在海灘散步：用方向鍵、搖桿或點地面讓皮普走動。每走一小段路，就會自動種下一朵花、用掉 1 片花瓣。Walk on the beach: move Pip with the arrow keys, the controller or by tapping the ground. Every few steps a flower is planted automatically, using 1 petal.
- 花的顏色：跟在皮普後面的精靈會決定花色。孵出越多精靈，花園就越繽紛（灰階鯨藍、四葉綠、磨磨黃、剪剪紅、縮縮橘……）。Flower colours: the sprites following Pip choose the colours. The more sprites you hatch, the more colourful the garden (Greyling blue, Clover green, Mopsy yellow, Snip red, Puffy orange…).
- 小規則：關卡平台上不會種花；沙灘最多保留約 420 朵，種滿後最舊的花會讓位給新花。花瓣用完就先去過關或重玩拿星星。Small rules: no flowers are planted on stage pads; the beach keeps about 420 flowers, and the oldest make room for new ones. Out of petals? Clear or replay a stage for more stars.
- 會存起來：種下的花會跟著存檔保存，破關畫面會顯示你種了幾朵。They are saved: your flowers are stored with your save, and the ending shows how many you planted.
🗼 關卡（對應 PCAM.02）Stages (PCAM.02)
- 2-1 灰階排行：原子序對比 C = (η₂ − η₁)/η₂、平均原子序 Z̄（s.7–8、13）2-1 Grey Ranking: atomic-number contrast C = (η₂ − η₁)/η₂ and mean Z̄ (s.7–8, 13)
- 2-2 四葉草偵測器：四象限 BSE 的相加與相減模式（s.11–12）2-2 Clover Detector: sum vs difference modes of a four-quadrant BSE detector (s.11–12)
- 2-3 磨磨的魔法：平均、中值濾波與背景校平（s.17–19）2-3 Mopsy's Magic: averaging, median filter and background levelling (s.17–19)
- 2-4 剪剪下刀：灰階直方圖與臨界值分割（s.20–21）2-4 Snip's Cut: grey-level histogram and thresholding (s.20–21)
- 2-5 河豚縮縮長長：侵蝕、膨脹、斷開與閉合（s.23–24、27）2-5 Puffy's Shrink & Grow: erosion, dilation, opening and closing (s.23–24, 27)
- 2-6 X 光水晶階梯：Kα／Kβ／Lα、EDS 峰辨識、過電壓 U 與 X 光產生範圍（s.35–43）2-6 X-ray Crystal Steps: Kα / Kβ / Lα, EDS peaks, overvoltage U and X-ray range (s.35–43)
- BOSS 影子菇：總複習，答對就發射 X 光彩虹光束BOSS Shadowshroom: review quiz; right answers fire the rainbow X-ray beam
關卡依序開放：過了前一層，下一層的平台才會發光。Stages open in order: a pad lights up once the previous one is cleared.
⭐ 星星與存檔Stars & saves
- 答錯不會失敗，可以一直重試。全對 3 顆星，錯 1–2 次 2 顆星，錯更多次 1 顆星；可重玩刷新最佳紀錄。Wrong answers never end the game; just try again. No mistakes = 3 stars, 1–2 mistakes = 2 stars, more = 1 star. Replay to beat your best.
- 過關會自動存檔；也可在「存檔／讀檔」存到槽位 1–3，或匯出成檔案帶到別台裝置。The game autosaves after every stage; you can also save to slots 1–3 or export a file to use on another device.
- 在關卡中存檔，讀檔後會從該關開頭開始。A save made inside a stage restarts that stage from its beginning.
📱 手機與全螢幕Phone & full screen
- 按「⛶ 全螢幕開始」最好玩；手機請橫向握持。“⛶ Full screen & play” works best; hold your phone sideways.
- 離開全螢幕：按右上角「✕ 離開全螢幕」，或在暫停選單按「✕ 離開全螢幕」，或在設定把全螢幕切成「關」。電腦上也可按 Esc。Leaving full screen: tap “✕ Exit” at the top right, or “✕ Exit full screen” in the pause menu, or switch Full screen off in Settings. On a computer, Esc also works.
- 全螢幕時畫面固定，不會被拖動或縮放。In full screen the view is locked: no scrolling or zooming.
🌊 World 2 全破！對比海灣恢復光彩World 2 clear! Contrast Cove shines again
下一站：World 3 水泥花園（PCAM.03）。Next stop: World 3, Cement Garden (PCAM.03).
AEML, NTUST
遊戲無法啟動The game could not start
此遊戲由 AEML, NTUST 製作。若程式碼遭到修改，或瀏覽器封鎖了 JavaScript，將無法執行。This game was created by AEML, NTUST. It will not run if its code has been modified or JavaScript is blocked.
HINTPAUSE
BA
AEML, NTUST
操作： 移動／調整 · 或 Enter 確定 · 返回 · 暫停 · 提示。也可以直接點選或拖曳畫面。請先點一下遊戲畫面，按鍵才會送進遊戲。Controls: move / adjust · or Enter confirm · back · pause · hint. You can also tap and drag on the screen. Click the game screen first so keys go to the game.
Micro Bloom World 2 | (c) 2026 AEML, NTUST | CT5812701 PCAM
皮普Pip
叮叮Zing
糊糊菇Blurshroom
影子菇Shadowshroom
灰階鯨Greyling
四葉Clover
磨磨Mopsy
剪剪Snip
縮縮Puffy
殼殼Shelly
碰碰Bonk
毛毛Fluffy
2-1 灰階排行2-1 Grey Ranking
2-2 四葉草偵測器2-2 Clover Detector
2-3 磨磨的魔法2-3 Mopsy's Magic
2-4 剪剪下刀2-4 Snip's Cut
2-5 河豚縮縮長長2-5 Puffy's Shrink & Grow
2-6 X 光水晶階梯2-6 X-ray Crystal Steps
BOSS 影子菇BOSS Shadowshroom
A：進入A: Enter
先完成前一關Clear the previous stage first
鋁 AlAluminium Al
鐵 FeIron Fe
鉑 PtPlatinum Pt
金 AuGold Au
偏高嶺土metakaolin
石灰石limestone
氫氧化鈣 CHportlandite (CH)
矽酸三鈣 C₃Salite (C₃S)
BSE 灰階排行（由暗到亮）BSE grey ladder (dark → bright)
Pt 比較亮Pt is brighter
Au 比較亮Au is brighter
幾乎看不出差別Almost no visible difference
SE 影像（E–T）SE image (E–T)
相加 A+B+C+DSum A+B+C+D
相減 A−BDifference A−B
··
平均 3×3Average 3×3
平均 11×11Average 11×11
中值濾波 3×3Median 3×3
背景校平Level background
重來Reset
雜訊Noise
邊緣清晰Edge sharpness
背景均勻Even background
臨界值Threshold
下刀CUT
灰階直方圖（暗 → 亮）Grey-level histogram (dark → bright)
孔隙率Porosity
水化物與 CH 的峰重疊了，這代表什麼？The hydrate and CH peaks overlap. What does that mean?
一定找得到完美的臨界值A perfect threshold always exists
一定會有像素被分錯，要報告不確定度Some pixels will be misclassified: report the uncertainty
縮（侵蝕）Shrink (erode)
長（膨脹）Grow (dilate)
顆粒數Features counted
L 層 → K 層L → K
M 層 → K 層M → K
M 層 → L 層M → L
OO
AlAl
SiSi
SS
CaCa
FeFe
加速電壓 E₀Beam energy E₀
鎖定LOCK
紫圈：X 光產生範圍 · 紅點：2 µm 富鐵夾雜物Purple: X-ray range · red: 2 µm Fe-rich inclusion
哪一種模式能顯示真正的成分？Which mode shows the true composition?
走到發光的平台，按 A 進入；在沙灘上散步就會開花！Walk to a glowing pad and press A. Flowers bloom as you walk on the sand!
哪一塊在 BSE 影像中比較亮？點選它。Which tile is brighter in a BSE image? Tap it.
依 BSE 亮度由暗到亮，依序點選四種水泥相。Tap the four cement phases in order, from dark to bright in BSE.
鉑和金放在一起，看得出差別嗎？Platinum next to gold: can you see a difference?
切換偵測模式，只顯示「成分」對比。Switch detector modes to show only compositional contrast.
現在只顯示「形貌」（凹凸）對比。Now show only topographic (bump) contrast.
哪一個亮點是真正的重元素相？可以切換模式檢查。Which bright spot is a real heavy phase? Switch modes to check.
去除雜訊，但要保留清楚的邊緣。Remove the noise but keep the edges sharp.
左邊較亮只是因為朝向偵測器：讓背景變均勻。The left side is brighter only because it faces the detector: make the background even.
拖動臨界值到孔隙峰與水化物峰之間的谷底，再按下刀。Drag the threshold to the valley between the pore and hydrate peaks, then CUT.
看看重疊的峰，選出正確的說法。Look at the overlapping peaks and pick the right statement.
讓顆粒數剛好是 3，而且顆粒要恢復原本大小。Make the count exactly 3, with the grains back to full size.
把裂開的纖維接回來：顆粒數剛好是 2，粗細不變。Join the cracked fibres: count exactly 2, original thickness.
產生 Kα X 光：哪一個電子跳躍？Make a Kα X-ray: which electron jump?
產生 Kβ X 光：哪一個電子跳躍？Make a Kβ X-ray: which electron jump?
產生 Lα X 光：哪一個電子跳躍？Make an Lα X-ray: which electron jump?
星號標示的峰，是哪個元素的 Kα？Which element's Kα is the starred peak?
調整 E₀：激發 Fe K（U ≥ 2），X 光範圍又要接近夾雜物大小（Rₓ ≤ 2.3 µm）。Set E₀ to excite Fe K (U ≥ 2) while keeping the X-ray range near the inclusion size (Rₓ ≤ 2.3 µm).
答對題目，大家一起發射 X 光彩虹光束！Answer correctly to fire the rainbow X-ray beam together!
影子菇把影像換成相減模式了！切換到正確的模式！Shadowshroom switched to difference mode! Pick the right mode!
移動：方向鍵、搖桿或點沙灘 · 確定：空白鍵／AMove: arrow keys, controller or tap the sand · Confirm: Space / A
已帶入 World 1 的夥伴與花瓣！Your World 1 friends and petals came along!
對！Fe 的原子序與 η 較大，所以比較亮。對比很大，很好分辨。Right! Fe has higher Z and η, so it is brighter. Big contrast, easy to see.
再想想：原子序越大，背散射電子越多。Think again: a higher atomic number means more backscattered electrons.
完全正確！偏高嶺土 < 石灰石 < CH < C₃S。Perfect! Metakaolin < limestone < CH < C₃S.
順序不對。卡片上已顯示平均原子序 Z̄，由小到大點選！Not that one. Each card now shows its mean Z̄: tap from smallest to largest!
沒錯！相鄰的重元素對比只有約 0.4%，要很大的電流和很慢的掃描才看得到。Correct! Adjacent heavy elements give only ~0.4% contrast; you need high current and a very slow scan to see it.
技術上 Au 稍亮，但對比只有約 0.4%，螢幕上幾乎看不出來！Technically Au is slightly brighter, but the contrast is only ~0.4%: almost invisible on screen!
η(Pt) 其實略小於 η(Au)，而且差異小到幾乎看不見！η(Pt) is actually slightly smaller than η(Au), and the difference is almost invisible!
相加模式：凹凸被抵銷，只剩成分（原子序）對比！Sum mode: the bumps cancel and only compositional (Z) contrast remains!
相減模式會抵銷成分、留下凹凸。換一個試試！Difference mode cancels composition and leaves the bumps. Try another!
SE 影像主要顯示形貌。成分要用 BSE 的哪一種模式？The SE image mostly shows topography. Which BSE mode shows composition?
相減模式：成分被抵銷，凹凸像被單側光照亮！Difference mode: composition cancels and the bumps look lit from one side!
相加模式顯示的是成分喔。要看凹凸，用另一種 BSE 模式。Sum mode shows composition. For the bumps, use the other BSE mode.
SE 也看得到形貌，但混了一點成分。BSE 相減模式最乾淨！SE shows topography too, but mixed with a little composition. BSE difference mode is cleanest!
對！切到相加模式它依然很亮，是真正的重元素相。Yes! It stays bright in sum mode, so it is a real heavy phase.
那是凸起的邊緣：在 SE 很亮，切到相加模式就不見了。That's a bump edge: bright in SE, but it vanishes in sum mode.
中值濾波：雜訊不見了，邊緣還是很清楚！Median filter: the noise is gone and the edges stay sharp!
平均範圍太大，雜訊沒了，邊緣也糊掉了！按「重來」再試。Averaging over that many pixels removes the noise and the edges too! Press Reset and try again.
好一點，但椒鹽雜點被抹成小斑塊，邊緣也變軟了。有更好的濾波器嗎？Better, but the salt-and-pepper specks smear into blobs and the edges soften. Is there a better filter?
校平改善了亮度不均，但雜訊還在。先處理雜訊！Levelling fixes uneven brightness, but the noise is still there. Deal with the noise first!
背景校平完成：同一個相在左右兩邊亮度一樣了！Background levelled: the same phase now has the same brightness on both sides!
這招不能修正左右亮度不均。試試另一個工具！That won't fix the left-right brightness trend. Try another tool!
漂亮的一刀！量到的孔隙率接近真實值：Clean cut! The measured porosity is close to the true value:
臨界值太低：孔隙邊緣沒算進去，孔隙率偏小。Threshold too low: pore edges are missed, so the porosity is too small.
臨界值太高：部分水化物也被當成孔隙了。Threshold too high: some hydrates are counted as pores.
對！峰重疊時，臨界值設在哪都會有像素分錯，所以要報告不確定度。Right! With overlapping peaks some pixels are misclassified wherever you cut, so report the uncertainty.
峰重疊時，不存在完美的臨界值。再想想！With overlapping peaks there is no perfect threshold. Think again!
全部縮不見了！按「重來」。Everything shrank away! Press Reset.
斷開成功：黏在一起的顆粒分開了，小雜點也消失了！Opening done: the touching grains separated and the specks vanished!
顆粒分開了！但變小了，再讓它們長回來。They're separated! But they shrank, so grow them back.
閉合成功：每條纖維都完整了，可以正確量測！Closing done: each fibre is whole again and can be measured correctly!
纖維接起來了！但變胖了，再縮回原本粗細。The fibres are joined! But they got fatter, so shrink them back.
正確！L → K 產生 Kα，是最強的 K 線。Correct! L → K gives Kα, the strongest K line.
正確！M → K 跨了兩層，產生能量較高的 Kβ。Correct! M → K jumps two shells and gives the higher-energy Kβ.
正確！空位在 L 層、由 M 層補上，就是 Lα。Correct! A vacancy in L filled from M gives Lα.
不對喔：字母是「空位所在的殼層」；α 表示從相鄰外層補位，β 表示跨兩層。Not quite: the letter is the shell with the vacancy; α means it is filled from the next shell out, β from two shells out.
答對！Correct!
再看看峰的能量位置：Check the peak energy again:
完美！Fe K 被激發，X 光範圍又接近夾雜物大小。Perfect! Fe K is excited and the X-ray range is close to the inclusion size.
過電壓不足：U < 2，Fe K 線太弱。提高電壓！Overvoltage too low: U < 2, so the Fe K lines are weak. Raise the voltage!
電壓太高：X 光範圍遠大於 2 µm，會量到周圍的漿體。Voltage too high: the X-ray range is much larger than 2 µm and samples the surrounding paste.
相加模式揭穿了幻術：影子消失，真正的相現形了！Sum mode breaks the illusion: the shadows vanish and the real phases appear!
這個模式還是被影子騙了！That mode is still fooled by the shadows!
提示：四片葉子相加，凹凸就會抵銷。Hint: add all four leaves and the bumps cancel.
命中！Hit!
先完成前一層！Clear the previous floor first!
已存檔至槽位Saved to slot
已讀取存檔。Save loaded.
這個槽位沒有存檔。That slot is empty.
已刪除存檔。Save deleted.
已匯出存檔檔案。Save file exported.
已匯入存檔。Save file imported.
存檔檔案不正確或已被修改。That save file is invalid or has been modified.
瀏覽器儲存空間不足，請改用匯出。Browser storage is full. Use Export instead.
此裝置無法使用 WebGPU，已改用軟體繪圖。WebGPU is not available here, so software rendering is used.
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這裡沒有額外提示，加油！No extra hint here. You can do it!
不太對喔，再試一次！Not quite. Try again!
要離開全螢幕，按右上角「✕ 離開全螢幕」或暫停選單。To leave full screen, tap “✕ Exit” at the top right or use the pause menu.
把手機橫過來，畫面會更大！Turn your phone sideways for a bigger screen!
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已暫停。Paused.
重新開始本關。Stage restarted.
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自動（依場景變換）Auto (changes with the scene)
開始新遊戲？自動存檔會被覆蓋（槽位 1–3 不受影響）。Start a new game? The autosave will be overwritten (slots 1–3 are kept).
回到標題畫面？本關未完成的進度會消失。Return to the title screen? Progress in this stage will be lost.
刪除這個存檔？Delete this save?
讀取這個存檔？目前未存檔的進度會消失。Load this save? Unsaved progress will be lost.
從頭開始新遊戲？自動存檔會被覆蓋。Start over with a new game? The autosave will be overwritten.
獲得花瓣Petals earned
新精靈孵化！New sprite hatched!
解鎖概念明信片：Postcard unlocked:
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種下的花Flowers planted
尚未孵化Not hatched yet
尚未解鎖：過關後取得Locked: clear the stage to get it
（空）(empty)
叮！花園綻放之後，我追著一道 X 光訊號，一路來到這片「對比海灣」。Ding! After the garden bloomed, I followed an X-ray signal all the way to Contrast Cove.
World 1 的夥伴都跟來了，花瓣也帶著！這片沙灘也能種花嗎？All our World 1 friends came along, and we brought our petals! Can we plant flowers on this beach too?
可以！不過……我得先告訴大家：海灣裡那些忽明忽暗的影子，是我表哥「影子菇」搞的。You can! But... I have to tell you something. Those flickering shadows in the cove are my cousin Shadowshroom's doing.
嘻嘻～亮的不一定重，暗的不一定輕！凹凸的影子和真正的成分，你們分得出來嗎？Hee-hee! Bright isn't always heavy, and dark isn't always light! Can you tell bumps from real composition?
我們要點亮「X 光水晶燈塔」：讀懂對比、把影像變成數字，最後認識特性 X 光，也就是我的家族！Let's light the X-ray Crystal Lighthouse: read contrast, turn images into numbers, and meet characteristic X-rays, my own family!
走到 2-1 的平台出發吧！Let's head to pad 2-1!
叮！微光花園綻放之後，我追著一道 X 光訊號，一路來到這片「對比海灣」。Ding! After the Micro Garden bloomed, I followed an X-ray signal all the way to Contrast Cove.
這台裝置上沒有 World 1 的存檔，不過夥伴們還是都來了！There's no World 1 save on this device, but our friends came along anyway!
我得先告訴大家：海灣裡那些忽明忽暗的影子，是我表哥「影子菇」搞的。I have to tell you something: those flickering shadows in the cove are my cousin Shadowshroom's doing.
嘻嘻～亮的不一定重，暗的不一定輕！凹凸的影子和真正的成分，你們分得出來嗎？Hee-hee! Bright isn't always heavy, and dark isn't always light! Can you tell bumps from real composition?
我們要點亮「X 光水晶燈塔」：讀懂對比、把影像變成數字，最後認識特性 X 光！Let's light the X-ray Crystal Lighthouse: read contrast, turn images into numbers, and meet characteristic X-rays!
走到 2-1 的平台出發吧！Let's head to pad 2-1!
噗咻～我是灰階鯨！BSE 影像裡，平均原子序越大、背散射係數 η 越大，看起來就越亮。Pfoosh! I'm Greyling! In a BSE image, the higher the mean atomic number and backscatter coefficient η, the brighter it looks.
兩相的對比 C = (η₂ − η₁)/η₂。大於約 10% 很好分辨；只有幾 % 就要加大電流、放慢掃描。The contrast between two phases is C = (η₂ − η₁)/η₂. Above about 10% it's easy; at only a few % you need more current and a slower scan.
水泥裡的相要算平均原子序：Z̄ = Σ wᵢZᵢ，wᵢ 是各元素的質量分率喔！For cement phases, use the mean atomic number Z̄ = Σ wᵢZᵢ, where wᵢ is each element's mass fraction!
我是四葉，四象限 BSE 偵測器！A、B、C、D 四片葉子各自收集背散射電子。I'm Clover, a four-quadrant BSE detector! My leaves A, B, C and D each collect backscattered electrons.
成分改變時，四片葉子收到的 BSE「數量」一起變；凹凸改變的是我們的「軌跡」，所以對面的葉子會意見不同！When composition changes, all four leaves get more or fewer BSE together; bumps change our trajectory, so opposite leaves disagree!
所以：相加 A+B+C+D → 成分對比；相減 A−B → 形貌對比。So: sum A+B+C+D → compositional contrast; difference A−B → topographic contrast.
我是磨磨，專門幫影像洗澡！但洗太用力，邊界也會被磨掉喔。I'm Mopsy, and I give images a bath! But scrub too hard and the edges wear away too.
平均濾波會讓邊緣變糊；中值濾波能去雜訊又保留邊緣。還有，背景校平要在設定臨界值之前做！Averaging blurs edges; a median filter removes noise but keeps them. And level the background before you threshold!
喀嚓喀嚓！我是剪剪。比臨界值暗的像素都會變成孔隙，在哪裡下刀，就決定量到多少孔隙率！Snip snip! I'm Snip. Every pixel darker than the threshold becomes pore, so where I cut decides the porosity!
看直方圖：孔隙峰和水化物峰之間的深谷，就是乾淨的下刀處。臨界值是一個決定，不是事實！Read the histogram: the deep valley between the pore peak and the hydrate peak is a clean place to cut. A threshold is a decision, not a fact!
呼——我是縮縮！我一縮，每個顆粒的邊緣就少一圈像素（侵蝕）；我一鼓，就多一圈（膨脹）。Phoo! I'm Puffy! When I shrink, each feature loses a ring of pixels (erosion); when I puff up, it gains one (dilation).
先縮再長＝斷開：分開黏在一起的顆粒、去掉小雜點。先長再縮＝閉合：把裂開的碎片接回來。Shrink then grow = opening: it separates touching grains and removes specks. Grow then shrink = closing: it joins broken pieces.
我是殼殼，身上有 K、L、M 三層殼。最裡面的 K 層最難剝，能量也最高！I'm Shelly, with K, L and M shells. The innermost K shell is the hardest to peel and the most energetic!
電子束把內層電子撞出去，外層電子跳下來補位，多出的能量就變成我：特性 X 光！The beam knocks out an inner electron, an outer electron drops into the hole, and the spare energy becomes me: a characteristic X-ray!
L 跳到 K 叫 Kα，M 跳到 K 叫 Kβ，M 跳到 L 叫 Lα。能量決定是哪個元素，強度決定有多少。L to K is Kα, M to K is Kβ, and M to L is Lα. Energy tells you which element; intensity tells you how much.
嘻嘻嘻！我把形貌的影子全偽裝成成分，你們的燈塔永遠亮不起來！Hee-hee! I've disguised every topographic shadow as composition. Your lighthouse will never shine!
大家一起上！每答對一題，就發射一道 X 光彩虹光束！Everyone together! Every right answer fires a rainbow X-ray beam!
看招！相減模式的影子幻術！Take this! The difference-mode shadow illusion!
別上當！切換到能顯示真正成分的模式！Don't fall for it! Switch to the mode that shows the true composition!
嗚……我一半在光裡、一半在影子裡，大家總是分不清哪個才是真正的我……Sniff... I'm half in light and half in shadow, and nobody can ever tell which part is really me...
表哥，我懂那種感覺！一起住到花園吧，在清楚的影像裡，沒有人會被誤會。Cousin, I know that feeling! Come live in the garden. In a clear image, nobody gets misunderstood.
燈塔亮了！下一站是「水泥花園」，那裡有 EDS、試片製備，還有好多水泥相精靈在等我們！The lighthouse is shining! Next stop: the Cement Garden, with EDS, specimen preparation and lots of cement-phase sprites waiting for us!
大家一起跳綻放之舞！Everyone, Bloom Dance!
Pt 與 Au 的原子序對比只有約 0.4%。要在影像中看出這個差異，需要什麼？The atomic-number contrast between Pt and Au is only about 0.4%. What do you need to see it?
加大電子束電流、放慢掃描，讓對比大於雜訊More beam current and a slower scan, so the contrast exceeds the noise
把螢幕亮度調高就好Just turn up the display brightness
把試片傾斜 60°Tilt the specimen to 60°
原始訊號中的對比必須大於雜訊才看得見；對比大於約 10% 很容易，只有幾 % 時需要大電流與慢掃描。傾斜反而會讓各元素的 η 趨於相近。（PCAM.02 s.5、8–9）Contrast in the raw signal must exceed the noise. Above ~10% is easy; a few % needs high current and slow scans. Tilting actually makes η of all elements converge. (PCAM.02 s.5, 8–9)
提示：螢幕只是把訊號翻譯出來，不會增加原始對比。Hint: the display only translates the signal; it cannot add contrast.
LC3 漿體裡一條裂縫邊緣在 BSE 影像中很亮。要怎麼證明它是富鈣的邊緣，而不只是邊緣效應？A crack edge in an LC3 paste looks bright in the BSE image. How would you prove it is a Ca-rich rim and not just an edge effect?
比較四象限偵測器的相加與相減模式，再用 EDS 做 Ca 的面分布或線掃描Compare the sum and difference modes of the four-quadrant detector, then map or line-scan Ca with EDS
把影像亮度調低，看它還亮不亮Lower the image brightness and see if it is still bright
換一個更大的光圈Use a larger aperture
成分改變 BSE 的數量（相加模式保留），形貌改變軌跡（相減模式保留）；X 光面分布則直接顯示元素。（s.10–13）Composition changes the number of BSE (kept in sum mode); topography changes their trajectory (kept in difference mode); an X-ray map shows the element directly. (s.10–13)
提示：要把「數量」和「軌跡」分開。Hint: separate the number component from the trajectory component.
為什麼要先做背景校平，再設定臨界值？Why level the background before setting a threshold?
讓同一個相在影像各處的亮度相同，同一個臨界值才適用全圖So the same phase has the same brightness everywhere, and one threshold works for the whole image
為了去除雜訊To remove noise
為了提高放大倍率To increase magnification
順序很重要：先校平再分割，先清理二值影像再量測。若影像間亮度／對比設定不同，臨界值就無法比較。（s.16–19）Order matters: level before thresholding, clean the binary image before measuring. If brightness/contrast change between images, thresholds cannot be compared. (s.16–19)
提示：破斷面一側較亮，只是因為它朝向偵測器。Hint: one side of a fracture looks brighter only because it faces the detector.
兩位同學用同一組影像，量出的孔隙率分別是 12% 和 18%。最可能的原因是？Two students get 12% and 18% porosity from the same images. What is the most likely reason?
臨界值設定不同：臨界值是一個決定，不是事實Different threshold settings: a threshold is a decision, not a fact
SEM 壞掉了The SEM broke
孔隙率會隨放大倍率自動改變Porosity changes automatically with magnification
應使用客觀的規則，例如累積直方圖的「溢流點」或反曲點，並固定擷取設定，才能重現。（s.20、30）Use an objective rule, such as the overflow or inflection point of the cumulative histogram, and fixed acquisition settings so results are reproducible. (s.20, 30)
提示：剛剛剪剪的刀子移一點點，孔隙率就變了。Hint: moving Snip's blade a little changed the porosity.
Delesse 原理 V_V = A_A = L_L = P_P 告訴我們什麼？What does the Delesse principle V_V = A_A = L_L = P_P tell us?
在隨機切面上，面積分率可以估計體積分率（不必假設顆粒形狀）On random sections, the area fraction estimates the volume fraction (no shape assumption needed)
所有顆粒都是球形All particles are spheres
2D 切面上的尺寸就等於 3D 尺寸Sizes on a 2-D section equal the 3-D sizes
分率可以信，尺寸要小心：不同的 3D 結構可能產生相同的 2D 切面，推估尺寸需假設形狀或用連續切片／斷層掃描。（s.27）Fractions are safe; sizes need care. Different 3-D structures can give identical 2-D sections, so sizes need a shape assumption or serial sections / tomography. (s.27)
提示：這是孔隙率能從影像得到的理由。Hint: it is why porosity can be measured from images.
Si Kα（1.740 keV）剛好高於 Al 的 K 吸收邊（1.560 keV）。在富含 Al 的相中會發生什麼？Si Kα (1.740 keV) lies just above the Al K edge (1.560 keV). What happens in an Al-rich phase?
Si X 光被 Al 強烈吸收、可能激發 Al 螢光，定量時需要 ZAF 校正Si X-rays are strongly absorbed by Al and may excite Al fluorescence, so quantification needs ZAF correction
Si 峰的位置會移動The Si peak shifts position
完全沒有影響Nothing happens
光子吸收是「全有或全無」：吸收改變的是強度，不是峰位。量到的強度 ≠ 產生的強度，所以要做 Z、A、F 校正。（s.40、46–48）Photon absorption is all-or-nothing: it changes intensity, not peak position. Measured intensity ≠ generated intensity, hence the Z, A and F corrections. (s.40, 46–48)
提示：剛好高於吸收邊一點點，最容易被吞掉。Hint: just above an absorption edge, X-rays are gobbled up most easily.
鋁與鐵之間的原子序對比 C 大約是多少？About how large is the atomic-number contrast C between Al and Fe?
約 0.45（很容易看出）About 0.45 (easy to see)
約 0.004About 0.004
正好 1.0Exactly 1.0
C = (η₂ − η₁)/η₂ ≈ 0.45；Pt／Au 相鄰元素才只有約 0.004。（s.8）C = (η₂ − η₁)/η₂ ≈ 0.45; only adjacent heavy elements such as Pt/Au drop to ~0.004. (s.8)
提示：灰階鯨第一題就算過了。Hint: Greyling calculated it in the very first round.
四象限 BSE 偵測器的「相加」模式主要顯示？The sum mode of a four-quadrant BSE detector mainly shows…
成分（原子序）對比Compositional (atomic-number) contrast
形貌對比Topographic contrast
X 光元素分布X-ray element maps
相加時凹凸互相抵銷；相減時成分互相抵銷。（s.12）In the sum the bumps cancel; in the difference the composition cancels. (s.12)
提示：四片葉子一起算。Hint: all four leaves together.
先侵蝕、再膨脹的運算叫做？Erosion followed by dilation is called…
斷開（opening），適合分開黏在一起的顆粒以便計數Opening, good for separating touching features before counting
閉合（closing）Closing
背景校平Background levelling
閉合則是先膨脹再侵蝕，用來填補縫隙、接回斷裂的碎片。（s.23–24）Closing is dilation then erosion, which fills gaps and joins broken parts. (s.23–24)
提示：縮縮先縮、再長。Hint: Puffy shrinks first, then grows.
量測顆粒時使用「保護框」是為了避免什麼？A guard frame for feature measurement avoids…
邊界偏差：大顆粒較容易被影像邊緣切掉而被低估Edge bias: large features are more often cut off by the image edge and under-represented
影像雜訊Image noise
試片充電Specimen charging
只量測右下角落在框內的顆粒，就能得到無偏的數量與尺寸分布。（s.28）Measure only features whose lower-right corner lies inside the frame to get unbiased counts and size distributions. (s.28)
提示：大朋友比較容易被相框切掉。Hint: big friends are more likely to be cut off by the frame.
Kα X 光是怎麼產生的？How is a Kα X-ray produced?
K 層有空位，由 L 層電子補上A K-shell vacancy is filled by an L-shell electron
K 層有空位，由 M 層電子補上A K-shell vacancy is filled by an M-shell electron
L 層有空位，由 M 層電子補上An L-shell vacancy is filled by an M-shell electron
M → K 是 Kβ，M → L 是 Lα；Kα 比 Kβ 強。（s.39）M → K is Kβ and M → L is Lα; Kα is more intense than Kβ. (s.39)
提示：α 表示從相鄰的外層補位。Hint: α means filled from the next shell out.
連續 X 光（制動輻射）在 EDS 能譜中扮演什麼角色？What role do continuous X-rays (bremsstrahlung) play in an EDS spectrum?
從 0 到 E₀ 的背景，定量前要扣除，也限制了微量元素的偵測A background from 0 to E₀ that must be subtracted and limits trace-element detection
用來辨識元素的尖峰Sharp peaks that identify elements
只在 E > E_c 時才出現They appear only when E > E_c
電子被原子的庫侖場減速，損失多少能量都有可能，所以是連續譜，上限是 E₀（Duane–Hunt 極限）。（s.32、34）Electrons slowed by the atoms' Coulomb field can lose any amount of energy, giving a continuum up to E₀ (the Duane–Hunt limit). (s.32, 34)
提示：急煞或輕煞，每次都甩出不同能量的閃光。Hint: brake hard or gently, and every stop throws off a different flash.
為什麼 X 光的空間解析度比 SE 差？Why is X-ray spatial resolution worse than SE resolution?
X 光在大部分交互作用體積內產生（約 µm 尺度），SE 只來自表面幾 nmX-rays come from most of the interaction volume (µm scale), SE only from the top few nm
X 光跑得比較慢X-rays travel more slowly
EDS 偵測器離得比較遠The EDS detector is farther away
取樣深度：SE 約 10 nm、BSE 約 450 nm、特性 X 光約 1 µm；15 kV 的「點」分析其實取樣約 2 µm。（s.43–45）Sampling depth: SE ~10 nm, BSE ~450 nm, characteristic X-rays ~1 µm; a 15 kV “point” analysis really samples ~2 µm. (s.43–45)
提示：X 光從淚滴深處大聲呼喊。Hint: X-rays shout from deep inside the teardrop.
中值（rank）濾波和平均濾波相比，有什麼優點？What is the advantage of a median (rank) filter over averaging?
能去除雜訊，又不會讓邊緣變糊It removes noise without degrading edges
讓影像更模糊It blurs the image more
會增加雜訊It adds noise
平均濾波的核越大，雜訊越少，但細節與邊緣也越少。（s.18–19）The larger the averaging kernel, the less noise but also the less detail and edge. (s.18–19)
提示：磨磨的第一關。Hint: Mopsy's first round.
在 EDS 中，X 光的「能量」和「強度」分別告訴我們什麼？In EDS, what do X-ray energy and intensity tell us?
能量辨識元素，強度用來定量Energy identifies the element; intensity quantifies it
強度辨識元素，能量用來定量Intensity identifies; energy quantifies
兩者都只能辨識元素Both only identify elements
能量只取決於元素種類；強度則受入射電子、厚度、吸收與濃度影響。（s.41）Energy depends only on the element; intensity depends on the incident electrons, thickness, absorption and concentration. (s.41)
提示：顏色告訴你是誰在說話，音量告訴你有多少人。Hint: colour tells you who is speaking; loudness tells you how many.
原子序對比 C = (η₂ − η₁)/η₂ · 平均原子序 Z̄ · 偏高嶺土、石灰石、CH、C₃S 排序（PCAM.02 s.7–9、13）Atomic-number contrast C = (η₂ − η₁)/η₂ · mean Z̄ · ranking metakaolin, limestone, CH and C₃S (PCAM.02 s.7–9, 13)
數量、軌跡、能量 · 四象限偵測器的相加與相減模式（s.6、11–12）Number, trajectory, energy · sum vs difference modes of a four-quadrant detector (s.6, 11–12)
平均與中值濾波 · 背景校平 · 處理順序（s.16–19）Averaging vs median filtering · background levelling · processing order (s.16–19)
灰階直方圖與臨界值分割 · 峰重疊與不確定度（s.20–21、30）Grey-level histogram and thresholding · overlapping peaks and uncertainty (s.20–21, 30)
侵蝕、膨脹、斷開、閉合 · Delesse 原理（s.23–24、27）Erosion, dilation, opening, closing · the Delesse principle (s.23–24, 27)
Kα／Kβ／Lα · 水泥 EDS 速查 · 過電壓 U 與 X 光產生範圍 · 吸收（s.35–47）Kα / Kβ / Lα · cement EDS cheat sheet · overvoltage U and X-ray range · absorption (s.35–47)
總複習：對比、影像分析與 X 光（s.5–48）Review: contrast, image analysis and X-rays (s.5–48)
交互作用體積精靈。這次要找出 X 光從淚滴多深的地方發出。The interaction-volume sprite. This time: how deep inside the teardrop do X-rays come from?
特性 X 光。每種元素一種顏色，World 2 的嚮導。A characteristic X-ray. One colour per element; your guide in World 2.
改邪歸正的糊糊菇，影子菇的表弟。The reformed Blurshroom, Shadowshroom's cousin.
灰階鯨。原子序越大越亮：C = (η₂ − η₁)/η₂。The grey-scale whale. Higher Z looks brighter: C = (η₂ − η₁)/η₂.
四象限 BSE 偵測器。相加看成分，相減看凹凸。A four-quadrant BSE detector. Sum for composition, difference for bumps.
影像海綿。中值濾波去雜訊又保留邊緣，還會背景校平。The image sponge. A median filter cleans noise but keeps edges, and Mopsy also levels backgrounds.
臨界值螃蟹。在直方圖的谷底下刀，臨界值是一個決定。The threshold crab. Cut in the histogram valley; a threshold is a decision.
形態學河豚。縮是侵蝕、鼓是膨脹，斷開與閉合靠順序。The morphology pufferfish. Shrink = erode, puff = dilate; opening and closing depend on the order.
K、L、M 殼層鸚鵡螺。Kα：L→K，Kβ：M→K，Lα：M→L。The K, L, M shell nautilus. Kα: L→K, Kβ: M→K, Lα: M→L.
一半在光、一半在影的影子菇。現在幫大家分辨成分與形貌。Half light, half shadow. Shadowshroom now helps everyone tell composition from topography.
📮 1 · 原子序對比Atomic-number contrast
C = (η₂ − η₁) / η₂ · Z̄ = Σ wᵢ Zᵢ
Al／Fe：C ≈ 0.45（容易）；Pt／Au：C ≈ 0.004（極難）。BSE 由暗到亮：偏高嶺土（Z̄ ≈ 10.7）< 石灰石（12.6）< CH（14.3）< C₃S（15.1）。成分影像要保持試片平整、不傾斜。Al/Fe: C ≈ 0.45 (easy); Pt/Au: C ≈ 0.004 (very hard). BSE dark → bright: metakaolin (Z̄ ≈ 10.7) < limestone (12.6) < CH (14.3) < C₃S (15.1). Keep the section flat and untilted for compositional imaging.
PCAM.02 s.5–9, 13
📮 2 · 成分 vs 形貌Composition vs topography
Sum A+B+C+D → Z · Difference A−B → topography
對比的三個組成：數量、軌跡、能量。成分改變 BSE 數量（四片同時變）；形貌改變軌跡（對面兩片不同）。SE 影像以形貌為主：δ = δ₀ sec θ。Contrast has three components: number, trajectory, energy. Composition changes the number of BSE (all segments together); topography changes trajectories (opposite segments disagree). SE images are mainly topographic: δ = δ₀ sec θ.
PCAM.02 s.6, 10–12
📮 3 · 影像前處理Image processing
Smooth → Level → Threshold → Open/Close → Measure
平均濾波：核越大越平滑，邊緣也越糊；中值濾波：去雜訊、保留邊緣；背景校平：讓同一相各處亮度一致。整組影像固定 kV、電流、WD、亮度與對比，存成無損 TIFF。Averaging: bigger kernels smooth more and blur edges; median: removes noise, keeps edges; levelling: same phase, same brightness everywhere. Fix kV, current, WD, brightness and contrast for the whole series; save lossless TIFF.
PCAM.02 s.15–19
📮 4 · 臨界值分割Thresholding
pixel size = field width / pixels per line
在直方圖兩峰之間的谷底下刀最乾淨；峰重疊時一定有像素被分錯，要報告不確定度。臨界值是一個決定，不是事實：用客觀規則（如溢流點）。Cut in the valley between two peaks; with overlapping peaks some pixels are always misclassified, so report the uncertainty. A threshold is a decision, not a fact: use an objective rule (e.g. the overflow point).
PCAM.02 s.16, 20–22, 30
📮 5 · 形態學與體視學Morphology & stereology
VV = AA = LL = PP · d = √(4A/π) · 4πA/P²
斷開＝侵蝕→膨脹（分開、去雜點，利於計數）；閉合＝膨脹→侵蝕（填縫、接回，利於量面積）。保護框避免邊界偏差。分率可信，尺寸要小心。Opening = erode → dilate (separate, remove specks, for counting); closing = dilate → erode (fill gaps, join pieces, for area). A guard frame avoids edge bias. Fractions are safe; sizes need care.
PCAM.02 s.23–29
📮 6 · 特性 X 光Characteristic X-rays
λ (nm) = 1.2398 / E (keV) · U = E₀ / Ec ≥ 2
Kα：L→K，Kβ：M→K，Lα：M→L。水泥常用 Kα：O 0.525、Al 1.487、Si 1.740、S 2.308、Ca 3.691、Fe 6.400 keV。Ca 需 E₀ ≥ 約 8 kV，Fe 需 ≥ 約 15 kV。Kα: L→K, Kβ: M→K, Lα: M→L. Cement Kα lines: O 0.525, Al 1.487, Si 1.740, S 2.308, Ca 3.691, Fe 6.400 keV. Ca needs E₀ ≥ ~8 kV, Fe ≥ ~15 kV.
PCAM.02 s.32–42
📮 7 · X 光範圍與吸收X-ray range & absorption
Rx = 0.064 (E₀1.68 − Ec1.68) / ρ [µm] · I/I₀ = exp[−(μ/ρ) ρ t]
方解石中的 Ca Kα：10 kV ≈ 0.9 µm、15 kV ≈ 2.0 µm、20 kV ≈ 3.4 µm。剛好高於吸收邊的 X 光最容易被吸收（Si Kα 被 Al 吸收），定量需 ZAF 校正。Ca Kα in calcite: 10 kV ≈ 0.9 µm, 15 kV ≈ 2.0 µm, 20 kV ≈ 3.4 µm. X-rays just above an absorption edge are absorbed most (Si Kα by Al), so quantification needs ZAF.
PCAM.02 s.43–48
綻放早晨 · PopBloom Morning · Pop
慵懶草原 · Lo-fi 輕鬆慵懶Lazy Meadow · Lo-fi (laid-back)
廚房律動 · Funk 節奏明快Kitchen Groove · Funk (upbeat)
寶石咖啡館 · Bossa nova 慵懶Gem Café · Bossa nova (laid-back)
像素星空 · 8-bit 晶片音樂Pixel Stars · 8-bit chiptune
果凍漂流 · SynthwaveJelly Drift · Synthwave
電子衝刺 · Rock 節奏明快Electron Rush · Rock (upbeat)
糖霜千層 · Bubblegum PopSugar Layers · Bubblegum pop
影子菇大決戰 · Hard rockShadowshroom Showdown · Hard rock
綻放之舞 · DiscoBloom Dance · Disco
明信片圓舞曲 · WaltzPostcard Waltz · Waltz
海灣衝浪 · Surf rock 節奏明快Cove Surf · Surf rock (upbeat)
鋼鼓沙灘 · Calypso 輕鬆慵懶Steel-drum Beach · Calypso (laid-back)
午後微風 · Reggae 輕鬆慵懶Afternoon Breeze · Reggae (laid-back)
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